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AD  NUMBER 


THIS  PAGE  IS  UNCLASSIFIED 


UD 

383 

H57 

1952 


T PC H N I C A L 
MEMORANDUM 
ORO-T  *160* 


UNCLASSIFIED 

Operational  Requirements 


U S ARMY  m»UTARY  HISTORY  INSTITUTE 
CARLISLE  BARRACKS,  PA  17013-5008 


(or 


an 


OPERATIONS  RESEARCH 

OFFICE 

• 

The  Johns  Hopkins 
University 


INFANTRY 
HAND  WEAPON 

By  Norman  Hitchman 

Statistical  Analysis  by  Scott  Forbush  and  George  Blakemore  Jr. 


This  document  is  now  unclassified,  as  shown  on  the 
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document,  all  markings,  other  than  UNCLASSIFIED, 
on  each  page  should  be  obliterated  so  that  there  is  no 
misunderstanding  of  the  current  classification  of  any 
information  derived  from  it. 


Operating  Under 
Contract  with  the 

DEPARTMENT  OF  THE 
ARMY 


FORMATION 


■* 


The  contents  of  ORO  publications , including  the  conclu- 
sions and  recommendations,  represent  the  Wews  of  ORO 
and  shou/d  not  be  considered  as  having  official  Depart- 
jnanf  of  the  Army  approval , either  expressed  or  implied . 


AWC  Form  1 Army— CGSC— P2-0236— 9 Aug  51— 25M 

vQ  Udv  KA 


ciw  contains  informahon  aflFec//ng  /he  na/iona/ 

defense  of  the  United  S fates  wi/hin  /he  mean/ng  of  /he 
Espionage  Laws,  Tide  7 8,  U.  S.  C.,  Sections  793  and  794. 
The  /ransmi'ss/on  or  /he  reve/adon  of  its  contents  in  any 
manner  to  an  unauthorized  person  is  prohibited  by  law . 


ATION 


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DOWNGRADED  AT  3 YEAR  INTERVALS: 

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DOD  DiR  5200.10 


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THIS  IS  A WORKING  PAPER 
Presenting  the  considered  results  of  study 
by  the  ORO  staff  members  responsible  for 
its  preparation.  The  findings  and  analysis 
are  subject  to  revision  as  may  be  required 
by  new  facts  or  by  modification  of  basic 
assumptions.  Comments  and  criticism  of 
the  contents  are  invited.  Remarks  should 
be  addressed  to:  , 

The  Director 

Operations  Research  Office 
The  Johns  Hopkins  University 
6410  Connecticut  Avenue 
Chevy  Chase,  Maryland 


' r 


4 ' 


LIBRAS  T 

ARMY  WAR  COLLEGE 


abstract  taken  by date 


mm 


UNUlftbMriLu, 


OPERATIONAL  REQUIREMENTS  FOR  AN  INFANTRY  HAND  WEAPON 

by 

Norman  A.  Hitchman 


Statistical  Analysis 

by 

Scott  E.  Forbush 
George  J.  Blakemore,  Jr. 


Of  what  should  a rifle  be  capable  in  battle  today?  Since  there  is  a 
limit/as  to  how  accurately  the  infantryman  fires,  can  one  increase  hits 
by  giving  him  a rifle  with  new  operational  characteristics?  ORO’s 
Project  BALANCE  studied  this  by  talcing  data  on  how  often,  and  by 
how  much,  riflemen  missed  targets  (as  well  as  the  distribution  of 
hits)  at  different  ranges,  by  talcing  data  on  the  ranges  of  engagement 
in  battle,  and  by  talcing  data  on  the  physiological  wound  effects  of 
shots  with  differing  ballistic  characteristics.  The  recommendation 
is  made  that  Ordnance  proceed  to  determine  the  technological 
feasibility  of  a weapon  with  operating  characteristics  analyzed  iii 
this  memorandum.  This  follows  from  conclusions  whjch  are  listed 
only  sketchily  below: 

Hit  effectiveness  using  the  M*1  is  satisfactory  only 

* up  to  100  yards  and  declines  very  rapidly  to  low 
order  at  300  yards,  the  general  limit  for  battlefield 
rifle  engagements. 

A pattern-dispersion  principle  in  the  hand  weapon 

• would  tend  to  compensate  for  human  aiming  errors 
and  increase  hits  at  ranges  up  to  300  yards. 

Missiles,  smaller  caliber  than  now  standard,  ‘could 
^ be  used  without  loss  in  wounding  effects  and  with 
logistical  advantage,  and  a great  increase  in  hit 
lethality  could  be  effected  by  using  toxic  missiles. 


Abstract  page  from:  O RO"  T- 1 60 

LASSIF 

(xM  + 105  pp,  51  Figs.,  11  Tables) 
Received:  19  dune  1952 

Proiect  BALANCE 


OPERATIONS  RESEARCH  OFFICE  — The  Johns  Hopkins  University 


IMfBM  CONlUd  WITH  1 H I D ■ M I I W E H T OF  THE  ARMY 


Log  No., 


81938 


Copy  No 


This  Document  contains  information  affecting  the  Nafiona/  Defense 
of  the  United  States  within  the  meaning  of  the  Espionage  Laws, 
Tit/e  IS,  U.S.C.,  Sections  793  and  794 . The  transmission  or  the 
reve/ation  of  its  contents  in  any  manner  to  an  unauthorized  person 
is  prohibited  by  law . 


THIS  ABSTRACT  IS  OF  A WORKING  PAPER 

Presenting  the  considered  results  of  study  by  the 
ORO  staff  members  responsible  for  its  preparation. 
The  findings  and  analysis  are  subject  to  revision  as 
may  be  required  by  new  facts  or  by  modification 
of  basic  assumptions.  Comments  and  criticism  of 
the  contents  are  invited.  Remarks  should  be  ad* 
dressed  to: 

The  Director 

Operations  Research  Office 
The  Johns  Hopkins  University 
6410  Connecticut  Avenue 
Chevy  Chase,  Maryland 


Technical  Memorandum  ORO-T-160 

^OPERATIONAL  REQUIREMENTS  FOR 
AN  INFANTRY  HAND  WEAPON 

by 

Norman  A^[itdiman 

Statistical  Analysis 

by 

Scott  E.  Forbush 
George  J.  Blake  mo  re,  Jr* 


LIBRARY 

ARMY  WAR  COLLEGE 
CARLISLE  BARRACKS,  PA. 

Received:  19  June  1952 

Project  BALANCE 


OPERATIONS  RESEARCH  OFFICE, 

jV  V|irj  ■ - ^ 

The  Johns  Hopkins  University. 

Chevy  Chase,  Maryland 


SECUI 


immmorn 


Unclassified 


U2> 


MS  7 


oc  LC&2.  tLf 


■ AYfY) 

v£\<*  b 

\ 


Published 
November  1952 
by 

OPERATIONS  RESEARCH  OFFICE 
6410  Connecticut  Avenue 


Unclassified 


ACKNOWLEDGMENT 


The  author  gratefully  acknowledges  the 
valuable  assistance  given  by  Col.  E.  M. 
Parker,  Project  Chairman,  in  the  prep- 
aration of  this  study;  especially  were  his 
paraphrases  welcomed,  for  they  crystal- 
lized areas  of  thought  where  otherwise 
the  author  would  have  faltered. 


CONTENTS 


Page 


ABSTRACT 

ACKNOWLEDGMENTS 

SUMMARY 

Purpose  — Assumptions  — Discussion  — Conclusions 
Recommendations. 

OPERATIONAL  REQUIREMENTS  FOR  AN  INFANTRY 
HAND  WEAPON 
Introduction 

COMBAT  CASUALTY  STUDIES 

Former  Studies  — Lethality  of  the  Rifle  — Rifle 
Bullet  Hits  as  a Function  of  Range  in  Combat  — 
Man-Rifle  Operations  Studies. 

TERRAIN  VISIBILITY  STUDIES 

Range  Requirements  and  Tactical  Employment 
of  Hand  Weapons  — Map  Analysis. 

THE  RIFLEMAN  AND  HIS  WEAPON 

Marksmanship:  Tests  and  Analyses  — The  Pattern 
Salvo  Weapon  — Full -Automatic  Fire  — Wound  Bal- 
listics: Missile  Caliber,  Mass,  and  Velocity. 

LETHALITY 

Weapons  in  General  — The  Rifle  — Comparison  of 
an  Ideal  Dispersion  Automatic  with  M-l  Single- 
Shot  Fire  — Can  Lethality  Be  Increased? 

THE  DISPERSION  WEAPON 

Basis  of  Issue  (T/O&E)  — Training  — Design 
Feasibility. 


5 

7 

10 

15 

25 

31 


ix 


CONTENTS  (Continued) 


Page 


A THEORY  FOR  DETERMINING  RELATIVE  EFFEC- 


TIVENESS  OF  DIRECT  FIRE  WEAPONS 
Method  Used. 

35 

CONCLUSIONS 

40 

REC  O MME  NDATIONS 

40 

BIBLIOGRAPHY 

42 

APPENDIX 

43 

Analysis  and  Application  of  Results  of  Rifle-Range 
Tests. 


FIGURES 

1.  Comparison  of  Battlefield  Visibility  in  Korea 

anrj  Ranges  of  Employment  of  the  M-l  Rifle.  10 

2.  Frequency  Distribution  for  Ranges  of  Contin- 
uous Visibility  for  Terrain  Classes  A,  B,  and  C.  12 

3.  Method  Used  in  Measuring  Range  of  Visibility 

on  Maps.  14 


4.  Marksmanship  Using  the  M-l  Rifle.  IV 

5.  Comparison  of  Lethality  per  Aimed  Shot  or 

Burst  for  the  M-l  and  the  Salvo  Automatic.  28 

6.  Rifle  Marksmanship,  Battlefield  Visibility, 

and  Hit  Probability  in  Combat.  37 

7.  Theoretical  Distribution  of  Hits  as  Function  of 

Range  for  M-l  Rifle  and  a Salvo-Type  Hand  Wea- 
pon for  Terrain  Classes  A,  C.  38 

8.  Relative  Effectiveness  of  M-l  Rifle  and  Salvo 

Automatic  for  Terrain  Classes  A,  C.  39 


UH  iOl* 


V i 

Cf  i 


du 


CONTENTS  (Continued) 


TABLES 

1.  Computed  Distribution  of  Hits  as  Function 
of  Range  R. 


2.  Relative  Effects  of  M-l  Single -Round  Fire 
and  Salvo  Fire  as  Function  of  Range  for 
Terrain  Classes  A and  C. 


Page 


36 


38 


xi 


SUMMARY 


PURPOSE 

The  study  reported  upon  in  this  memorandum  was  undertaken 
for  the  purpose  of  determining  the  desirable  operational  char- 
acteristics of  a general  purpose  infantry  hand  weapon. 


ASSUMPTIONS 

It  has  been  assumed  that  it  is  desirable  to  increase  in  both 
number  and  rate  the  hits  which  may  be  inflicted  on  the  enemy  by 
aimed  small  arms  in  the  hands  of  the  infantry. 

It  has  been  further  assumed  that  it  is  desirable  also  to 
increase  the  mortality  of  wounds  caused  by  these  hits. 


DISCUSSION 

In  this  examination  of  the  basic  infantry  weapon,  the  rifle, 
two  commonly  accepted  considerations  or  premises  were  care- 
fully scrutinized,  and  their  bearing  upon  infantry  operations 
evaluated:  1)  the  time  taken  to  hit  enemy  man  targets  is  vital 
in  that  hits  should  be  inflicted  as  early  and  at  as  great  a range 
as  possible;  and  2)  these  hits  should  inflict  significant  injury — 
should  be  at  least  immediately  incapacitating  (in  some  circum- 
stances, lethal).  The  findings  are  generally  affirmative  with 
respect  to  both  propositions. 

Study  of  combat  records  of  operations,  as  well  as  field 
investigations  of  the  man-rifle  combination,  shows  that  much  is 
to  be  gained  by  increasing  the  hit  capability  of  aimed  rifle  fire 
at  the  common  battle  ranges,  and  that  increasing  the  severity  of 
the  hits  is  also  to  be  sought.  How  men  actually  use  the  rifle  in 
combat,  the  ranges  of  engagement  most  frequently  recurring 
in  battle,  how  terrain  limits  inter  visibility  of  opposing  firing 


SECURI^^f^jMBfMRlFOetAATION 


lines,  and  what  is  required  ballistically  to  create  physiologically 
desirable  wound  effects  on  the  enemy,  are  factors  which  have 
been  analyzed  for  the  purpose  of  determining  the  operational 
requirements  of  a general  purpose  hand  weapon. 

Study  of  the  various  factors  involved  has  yielded  a number 
of  independent  but  related  and  consistent  determinations.  Syn- 
thesis has  permitted  comprehensive  evaluation  of  the  combat 
actions  bearing  in  concert  upon  effective  employment  of  the 
hand  weapon. 

Battlefield  visibility  data  show  why  combat  rifle  fire  is 
actually  so  limited  in  range  by  normal  terrain  obstructions  to 
the  line  of  sight  as  rarely  to  exceed  300  yd.  Studies  of  the 
manner  in  which  gunshot  wounds  are  incurred  in  battle  suggest 
that  lesser -included  ranges  are  in  reality  the  important  ones. 
Measurements  of  marksmanship  show  that  performance  is  of 
a very  low  order  beyond  a range  of  300  yd.  Wound  ballistic 
data  offer  convincing  evidence  that  small  caliber,  high  velocity 
missiles  may  be  used  profitably  at  such  ranges,  without  loss 
in  wounding  effects  and  with  significant  logistical  gains. 

The  mutually  confirmatory  nature  of  the  several  findings 
goes  far  to  explain  present  rifle  operations,  and  to  suggest  the 
desirable  characteristics  for  a general  purpose  infantry  hand 
weapon.  The  conclusions  which  follow  have  emerged. 

CONCLUSIONS 

1.  The  ranges  at  which  the  rifle  is  used  most  frequently  in 
battle  and  the  ranges  within  which  the  greater  fraction  of  man 
targets  can  be  seen  on  the  battlefield  do  not  exceed  300  yd. 

2.  Within  these  important  battle  ranges,  the  marksmanship 
of  even  expert  riflemen  is  satisfactory  in  meeting  actual  battle 
requirements  only  up  to  100  yd;  beyond  100  yd,  marksmanship 
declines  sharply,  reaching  a low  order  at  300  yd. 

3.  To  improve  hit  effectiveness  at  the  ranges  not  covered 
satisfactorily  in  this  sense  by  men  using  the  M-l  (100  to 
300  yd),  the  adoption  of  a pattern-dispersion  principle  in  the 
hand  weapon  could  partly  compensate  for  human  aiming  errors 
and  thereby  significantly  increase  the  hits  at  ranges  up  to  300  yd. 

4.  Current  models  of  fully  automatic  hand  weapons  afford 
neither  these  desirable  characteristics  nor  adequate  alterna- 
tives. Such  weapons  are  valueless  from  the  standpoint  of 
increasing  the  number  of  targets  hit  when  aiming  on  separated 
man- size  targets. 


2 


ORO-T-160 


SlWiT^^fPflfjy^TpTOiM  ATIO  N 


5.  Certain  of  tl 


ccuracy  observed 


in  the  manufacture  of  current  rifles  and  ammunition  can  be 
relaxed  without  significant  losses  in  over -all  hit  effectiveness. 

6.  To  meet  the  actual  operational  requirements  of  a general 
purpose  infantry  hand  weapon,  many  possibilities  are  open  for 


panying  increases  in  hit  probability)  at  the  ranges  of  interest. 

Of  the  possible  salvo  or  volley  automatic  designs,*  the  small 
caliber,  lightweight  weapon  with  controlled  dispersion  char- 
acteristics appears  to  be  a promising  approach.  (Low  recoil 
of  a small  caliber  weapon  facilitates  dispersion  control.) 

7.  To  create  militarily  acceptable  wound  damage  at  common 
battle  ranges,  missiles  of  smaller  caliber  than  the  present  stand- 
ard .30  cal  can  be  used  without  loss  in  wounding  effects  and  with 
substantial  logistical  and  over -all  military  gains. 

8.  A very  great  increase  in  hit  lethality  can  be  effected  by 
the  addition  of  toxic  agents  to  bullet  missiles. 

RECOMMENDATIONS 

1.  It  is  recommended  that  the  Ordnance  Corps  proceed  to 
determine  the  design  or  technological  feasibility  of  developing 
a hand  weapon  which  has  the  characteristics  cited  in  this 
analysis,  namely: 

a.  Maximum  hit  effectiveness  against  man  targets 
within  300  yd  range.  (This  does  not  mean  that  the  weapon  will 
be  ineffective  beyond  this  range.  ) 

b.  Small  caliber  (less  than  .30). 

c.  Wounding  capability  up  to  300  yd  at  least  equivalent 
to  the  present  rifle. 

d.  Dispersion  of  rounds  from  salvos  or  burst  controlled 
so  as  to  form  a pattern  such  that  aiming  errors  up  to  300  yd 

^Current  military  usage  of  the  two  words  salvo  and  volley  is  confused.  By  “salvo”  the 
Navy  and  Air  Force  generally  mean,  respectively,  the  simultaneous  discharge  of  several 
pieces,  or  the  simultaneous  release  of  a number  of  bombs;  the  Army  usually  employs  the 
word  to  indicate  the  successive  firing  of  several  guns  within  a single  command  unit. 
“Volley”  is  commonly  taken  by  all  services  to  mean  the  simultaneous  firing  of  a number 
of  rifles  or  guns,  with  the  exception  that  the  artilleryman  often  applies  the  word  to  the 
independent  (unsynchronized)  firing  of  a certain  specified  number  of  rounds  by  each  of 
several  associated  pieces.  What  is  discussed  here  and  in  the  following  pages  is  either 
a simultaneous,  or  a high  cyclic  rate,  burst,  with  the  number  of  rounds  per  burst  auto- 
matically set  rather  than  dependent  upon  trigger  release.  In  the  former  design,  con- 
trolled nutation  of  the  rifle  muzzle  would  provide  the  desired  shot  dispersion  or  pattern; 
in  the  latter,  the  scatter  would  be  obtained  and  controlled  by  multiple  barrels,  a mother- 
daughters  type  of  projectile,  or  projection  of  missiles  in  the  manner  of  a shotgun. 


designs  which  will  give  desirable  dispersion  patterns  (and  accom- 


ORO-T-160 


j 


3 


SECURITY, 


SECURITY-, 


^FORMATION 


Unclassified 

will  be  partly  compensated,  and  hit  effectiveness  thereby 
increased  for  these  ranges. 

2.  As  one  possible  alternative  to  the  current  "volume  of 
fire"  (fully  automatic)  approach  to  the  problem  of  increasing 
the  effective  firepower  of  infantry  riflemen,  it  is  recommended  — subject 
to  tentative  confirmation  of  design  feasibility— that  a rifle  incor- 
porating at  least  in  principle  the  military  characteristics  here 
proposed  be  manufactured  for  further  and  conclusive  test. 


jject 


OPERATIONAL  REQUIREMENTS  FOR  AN  INFANTRY 

HAND  WEAPON 

(INTRODUCTION 

The  subject  of  this  study  is  of  a basic  nature  for  it  applies 
to  the  basic  weapon  of  the  basic  branch— the  rifle  carried  by  the 
infantry.  Because  the  hand  arm  offers  certain  capabilities  not 
duplicated  by  any  other  means,  and  because  it  is  basic  to  the 
whole  weapons  system,  the  effectiveness  of  that  weapon  in  battle 
is  a subject  of  first  importance  in  any  general  consideration  of 
the  whole  fire  system.  It  follows  that  any  study  directed  toward 
a comprehensive  examination  of  the  aggregate  of  weapons  for  the 
purpose  of  designing  and  proportioning  a “balanced"  system 
(the  mission  of  Project  BALANCE)  may  logically  take  a beginning 
with  this  basic  ground  weapon. 

Such  an  approach  is,  moreover,  timely  at  the  moment  in  the 
sense  that  the  NATO  is  confronted  now  by  an  urgent  requirement 
for  standardization  of  a general  purpose  hand  weapon  for  the 
infantry.  Thus,  any  information  which  may  be  cogently  pertinent 
to  such  weapons  will  have  a bearing  on  an  immediate  problem  of 
some  moment. 

The  study  here  presented  has  been  carried  out  not  only  in 
full  recognition  of  the  importance  of  improving  the  effectiveness 
of  infantry,  but  also  in  growing  awareness  that  the  task — even 
though  so  basic  in  nature— is  an  exceedingly  complex  one.  The 
effort  has  thus  far  been  only  preliminary.  Limited  time,  and 
inadequate  knowledge  of  basic  unit  operations  in  combat,  have 
restricted  the  degree  to  which  the  whole  problem  might  be 
examined.  Consequently,  no  complete  solution  is  offered  by  this 
memorandum;  rather,  some  analytical  findings  are  presented, 
which  suggest  the  principles  governing  certain  measures  which 
could  be  undertaken  to  improve  infantry  effectiveness  with 
respect  to  aimed  rifle  fire. 

This  memorandum  bears  directly  upon  the  importance  and 
the  use  by  infantry  of  aimed  small  arms  fire  in  the  front  line 


ORO-T-160 


5 


IMATION 


Unclassil 


tactical  fire  fight,  but  does  not  consider  expressly  the  impor- 
tance, the  techniques  or  the  effects  of  unaimed  u covering  fire1’ 
delivered  by  small  arms.  The  reason  for  directing  the  study 
effort  toward  aimed  fire  is  that  the  common  arm  of  the  infantry, 
the  rifle,  is  designed  primarily  for  the  aimed  fire  role;  that  is, 
the  weapon  is  designed  expressly  to  afford  a capability  of  directing 
missiles  at  observed  man-targets  with  high  inherent  precision, 
in  both  offensive  and  defensive  action.  Delivery  by  such  a weapon 
of  covering  fire  to  neutralize  or  pin  down  the  enemy  and  permit 
friendly  maneuver  is  tactically  useful,  but  nonetheless  amounts 
to  a secondary  role  for  which  design  has  provided  only  inciden- 
tally, The  important  question  at  hand,  therefore,  is  not  so  much 
connected  with  the  varying  actual  use  of  the  present  firearm  as 
with  the  need  of  the  infantry  to  engage  the  close  enemy  effec- 
tively by  the  use  of  aimed  rifle  fire,  and  with  the  feasibility  of 
incorporating  in  the  rifle  of  general  issue  the  capability  of 
answering  this  real  requirement. 

Recent  ORO  investigations  in  Korea  have  shed  some  light 
on  this  subject  by  indicating  quantitatively  the  comparative 
importance  of  aimed  and  unaimed  fire  as  related  to  offensive 
and  defensive  operations.  Generally,  aimed  fire  plays  a more 
important  part  in  defense  than  unaimed  or  volume  fire,  whereas 
in  the  offensive,  the  reverse  is  true  Almost  irrespective  of 
the  part  played  by  the  supporting  weapons  before  or  during  the 
final  phase  of  close  combat,  the  decision  in  each  small  tactical 
battle  rests  ultimately  in  large  measure  with  the  infantryman 
and  his  ability  to  use  his  hand  weapon  effectively.  If  hand-to-hand 
fighting  develops  at  all,  decision  thus  rests  almost  entirely  with 
the  infantry  in  this  last  time -phase  of  the  tactical  situation.  To 
attach  importance  to  this  aspect  of  battle  is  therefore  logical, 
and  the  attempt  to  maximize  the  capability  of  infantry  in  this 
role  cannot  be  misdirected  effort. 

The  study  has  yielded  suggestions  for  increasing  infantry 
effectiveness  by  improving  the  effects  of  aimed  rifle  fire.  It 
appears  almost  certain  that  future  large-scale  ground  operations 
will  involve  a numerically  superior  enemy  and  necessitate,  at 
first,  a defensive  strategy  on  our  part.  Morever,  frequent 
attempts  to  overrun  infantry  positions,  with  attendant  close 
combat,  are  to  be  anticipated.  Thus,  to  increase  each  infantry  - 


highly  desirable. 

In  the  light  of  such  considerations  as  these,  it  appears  correct 
to  assume  that:  1)  it  is  desirable  to  increase  in  both  number  and 


man's  capability  with  respect  to  defensive  rifle  fire  becomes 


6 


1 


ORO-T-160 


ified 

rate  the  hits  which  may  be  inflicted  on  the  enemy  by  aimed  small 
arms  in  the  hands  of  the  infantry;  2)  it  is  also  desirable  to  increase 
the  mortality  from  wounds  caused  by  these  hits. 

The  research  effort  has  included  examination  of  casualties 
of  past  wars,  studies  of  terrain  as  it  limits  battlefield  visibility, 
determination  of  the  marksmanship  of  men,  wound  ballistics 
requirements,  actual  use  of  the  rifle  in  combat,  and  other 
considerations  bearing  on  military  operational  requirements 
for  the  general  purpose  hand  weapon.  The  determinations 
arrived  at  from  the  study  of  present  rifle  fire  and  its  effects 
are  presented  in  the  following  sections. 


I 


COMBAT  CASUALTY  STUDIES 


Former  Studies 

Earlier  work  done  by  ORO  on  the  defense  of  the  individual  in 
combat,1  and  a preliminary  study  of  the  offensive  capabilities 
of  the  rifle,2  yielded  definite  indications  that  rifle  fire  and  its 
effects  were  deficient  in  some  important  military  respects,  and 
that  further  study  of  the  problem  would  be  necessary  fully  to 
establish  the  facts.  In  these  former  studies  it  was  found  that, 
in  combat,  hits  from  bullets  are  incurred  by  the  body  at  random: 
regional  distribution  of  bullet  hits  was  the  same  as  for  fragment 
missiles  which,  unlike  the  bullet,  are  not  "aimed.  " Further, 
it  was  found  that  exposure  was  the  chief  factor  responsible  for 
the  distribution  of  hits  from  bullets  and  that  aimed  or  directed 
fire  does  not  influence  the  manner  in  which  hits  are  sustained.31 
Stated  briefly,  the  comparison  of  hits  from  bullets  with  those 
from  fragments  showed  that  the  rifle  bullet  is  not  actually  better 
directed  towards  vulnerable  parts  of  the  body. 

The  discovery  of  these  facts,  along  with  evidence  of  prodi- 
gious rifle  ammunition  expenditure  per  hit,  strongly  suggested 
the  need  to  extend  the  study  of  the  rifle  problem.  The  facts 
known  at  this  point  also  prompted  one  to  regard  with  some 
dubiety  the  employment  of  the  present,  highly  accurate,  pre- 
cision-made rifle  as  a general  purpose  infantry  weapon.  It 
should  be  noted,  .however,  that  complete  verification  would  not 
suggest  elimination  of  a precision  long-range  rifle  to  be  used 

‘Footnote  numbers  refer  to  publications  listed  in  Bibliography. 

Multiple  hits  on  the  same  target  are  much  less  to  be  desired  than  a large  number  of 
targets  hit. 


ORO-T-160 


7 


by  some  men  highly  skilled  and  selected  for  specialist  opera- 
tions, e.  g.  , snipers. 

Lethality  of  the  Rifle 

As  for  the  combat  importance  of  hits  from  rifle  bullets  as 
compared  to  other  weapons  in  the  ground  system,  historical 
studies  show  that  bullets  have  accounted  for  10  to  20  percent 
of  all  hits  from  all  ground  weapons  in  most  battles,  campaigns,  and 
wars  of  this  century.4  Although  these  figures  qualitatively  provide 
a measure  of  the  relative  capability  of  hitting  the  opposed  infantry- 
man, they  do  not  disclose  capabilities  with  respect  to  severity  of 
injury.  Of  these  two  factors  (simple  wounding  and  extent  of  injury) 
which  characterize  weapons  effects,  not  much  is  known  about  either 
in  the  sense  of  cost  versus  effect  because  ammunition  expenditures 
and  corresponding  casualty -producing  effects  are  not  usually  known 
with  precision.  On  the  other  hand,  aside  from  the  closely  related 
machine  gun,  the  rifle  is  the  most  lethal  of  all  conventional  ground 
arms:  its  lethal  index  (ratio  of  kills  to  hits)  exceeds  30  percent, 
putting  it  above  other  weapons  in  capability  of  inflicting  severe 
injury.*  The  lethal  index  of  the  machine  gun,  of  course,  exceeds 
that  of  the  rifle  because  multiple  hits  increase  over -all  lethality. 
For  bullet  lethality,  the  30  percent  figure  given  for  the  rifle  would 
be  the  closest  approximation  to  single  round  lethality  for  all  ranges 
in  battle . 

Rifle  Bullet  Hits  as  a Function  of  Range  in  Combat 

Knowledge  of  the  ranges  at  which  hits  have  been  incurred  in 
past  wars  is  sharply  limited.  Since  this  parameter  is  almost  indis- 
pensable to  the  military  specialist  or  operations  analyst  in  deter- 
mining weapons  effects,  it  is  astonishing  that  greater  efforts  in  the 
past  have  not  been  directed  toward  gathering  information  of  this 
kind  in  combat  operations. 


*In  this  analysis,  the  figure  30  percent  refers  only  to  enemy  weapons  of  World  War  II 
type  but  since  enemy  rifles  did  not  differ  greatly  from  our  own,  the  lethal  index  value 
should  approximate  that  of  the  M-l  rifle.  Strictly,  lethal  refers  here  to  the  bullet,  rather 
than  the  rifle,  which  is  the  launcher.  What  is  meant  is  that  a larger  fraction  of  the  total 
bullet  hits  results  in  death  than  from  hits  from  any  other  weapon.  The  explanation  does 
not  lie  in  the  manner  in  which  rifle  bullets  are  directed,  since  data  show  that  bullet 
hits  occur  on  the  body  at  random  just  as  do  hits  from  fragmenting  projectiles  and  there- 
fore their  relatively  high  lethality  is  not  connected  with  any  bias  in  their  distribution 
over  the  body.  The  reason  appears  to  be  connected  with  the  higher  (and  more  nearly 
constant)  energy,  on  the  average,  than  other  missiles  since  they  are  discharged  at  short 
ranges.  Fragments,  however,  vary  in  energy  from  a maximum  to  zero,  with  the  mean 
value  being  relatively  low  because  of  the  preponderance  of  small  fragments  per  missile 
burst  and  because  of  the  rapid  deceleration  of  particle  velocities  with  range. 


ORO-T-160 


* 


Unclassified 


Only  two  studies  exist  which  have  reference  to  bullet  hits  as 
a function  of  range  in  battle,  and  they  are  based  on  indirect  and 
possibly  inaccurate  measurements.  Oughterson®  analyzed  expe- 
rience on  Bougainville  in  World  War  II  and  found  that,  of  those 
cases  studied,  almost  all  rifle  bullet  hits  were  received  at  ranges 
less  than  75  yd.*  The  Surgeon  General  recently  examined  the 
wounded  in  Korea,  and  from  a sample  of  109  rifle  bullet  hits 
suffered  among  members  of  the  Turkish  Brigade,  the  mean  range 
for  these  hits  was  found  to  be  just  over  100  yd.*  It  was  noted, 
however,  that  most  of  the  hits  occurred  at  ranges  within  300  yd 
and  in  a later  section  of  this  report  these  data  along  with  data  on 
battlefield  visibility  will  be  given  more  extensive  treatment. 

Man-Rifle  Operations  Studies 

The  British  AORG  during  World  War  II,  and  ORO  in  FECOM, 
have  both  attempted  to  study  part  of  the  man-rifle  complex  by 
interviewing  experienced  riflemen  on  their  use  of  the  weapon  in 
offensive  and  defensive  combat  actions.  The  British  examined 
officers  and  NCOs  who  had  experience  in  the  ETO  7 and  ORO 
examined  men  with  experience  in  Korea.8  The  agreement  of  the 
two  independent  studies  is  striking.  For  attack  and  defense  in 
European  actions,  it  was  found  that  about  80  percent  of  effective 
rifle  and  LMG  fire  takes  place  at  less  than  200  yd  and  90  percent 
at  less  than  300  yd,  according  to  the  estimates  made  by  the  men 
interviewed.  About  90  percent  of  the  LMG  fire  was  at  less  than 
300  yd. 

Of  602  men  questioned  about  use  of  the  M-l  rifle  in  Korea, 

87  percent  said  that  at  least  95  percent**  of  all  their  firing  was 
done  at  targets  within  300  yd  range  (day  time  offensive  fighting)." 
For  day  time  defensive  fighting,  80  percent  of  the  men  said  that 
rifles  were  used  at  300  yd  or  less.  Figure  1 shows  the  frequency 
in  which  rifles  are  used  as  a function  of  range,  based  on  responses 
of  interrogated  infantrymen.  The  approximate  correspondence  of 
the  curves  in  the  Figure  indicates  that  the  use  of  the  rifle  is  to  at 
least  some  extent  dependent  upon  battlefield  terrain  features  as 
they  affect  visibility.***  Although  it  is  freely  acknowledged  that 
the  use  of  data  derived  from  judgments  of  the  men  about  the  use 
of  their  basic  arm  may  be  subject  to  question,  the  validity  of  the 

* 

This  figure  is  perhaps  atypically  low  because  it  refers  to  jungle  fighting  in  which 
^visibility  was  abnormally  restricted. 

The  men  were  asked  to  give  the  outside  limit  of  95  percent  of  their  firing  in  order  to 

eliminate  those  rare  shots  which  might  be  fired  at  long  ranges  without  expectation  of 
^ hitting  the  target. 

See  section  on  battlefield  visibility. 


aamfaS£CRFT  iiirnniii—i 

f I 


r*  . _ ■ 
j J3QCJ 

vj  ■ { , ; j ! 

L/  1 u 

O i 

X ia  ;&  1.  J * 3 

opinion  survey  has  been  substantiated  by  a more  recent  Korean 
study  conducted  in  combat  areas.5  Also,  as  mentioned  earlier, 
the  analysis  made  by  AORG  tends  to  support  the  conclusion  that 


Fig.  1 — Comparison  of  battlefield  visibility  in  Korea  and  ranges  of 
employment  of  the  M-l  Rifle. 


the  infantry  basic  weapon  is  actually  used,  on  the  average,  at 
shorter  ranges  than  commonly  believed. 

TERRAIN  VISIBILITY  STUDIES 

Range  Requirements  and  Tactical  Employment  of  Hand  Weapons 
Despite  the  important  role  of  infantry  support  weapons  (artil- 
lery,  tactical  aviation,  armor,  and  others),  the  entire  ground 
weapon  system  hinges  in  many  important  ways  upon  those  weapons 
which  depend  for  their  effective  employment  upon  ground  obser- 
vation  of  the  target.  These  are  the  direct-fire  and  observed-fire 
weapons;  they  are  elemental,  basic,  and  indispensable  to  the 
infantry-artillery-armor  team. 

Unclassifie 


ORO-T-160 


wmr  TnfohmatiS 


I I 


tf**. 


3d 


For  infantry,  the  basic  direct  fire  weapon  is  the  rifle— it  is 
the  common  denominator  upon  which  the  entire  fire  system  is 
designed,  both  physically  and  tactically.  Yet  all  direct-fire 
weapons  suffer  a major  weakness  in  that  essential  observation 
for  their  effective  employment  may  be  obscured  by  weather 
conditions,  prevented  by  darkness  or— more  importantly  and 
quite  unavoidably— interrupted  by  terrain  features.  This  inter- 
ruption of  the  line  of  sight  is  one  of  the  principal  military  effects 
of  terrain,  for  the  ranges  at  which  points  on  the  ground  are  inter - 
visible  are  related  to  the  employment  and  general  effectiveness 
of  these  direct-fire  weapons.  Accordingly,  terrain  limitations  to 
continuous  visibility  on  the  battlefield  should  dictate  to  a consid- 
erable degree  the  actual  design  and  employment  of  direct-fire  or 
observed-fire  weapons.  A study  of  this  subject  which  was  under- 
taken by  Project  BALANCE  and  which  is  covered  in  detail  in  a 
separate  report,10  has  yielded  formulary  expressions  for  the 
relationship  between  the  opening  range  of  engagement  for  riflemen 
and  the  range  at  which  man-targets  can  be  seen.  Particularly  with 
respect  to  the  rifle,  the  study  is  basic  in  its  concept  and  possibly, 
for  the  first  time,  data  have  been  obtained  which  constitute  a 
reasonable  quantitative  basis  for  determining  the  actual  range 
requirements  and  tactical  employment  of  a general-purpose 
hand  arm. 

Because  of  the  importance  of  these  findings  to  the  infantry 
weapons  problem,  they  should  be  studied  carefully  in  conjunction 
with  the  work  presented  here  on  operational  requirements  for  an 
infantry  hand  weapon. 


Map  Analysis 

Topographical  map  studies  of  a number  of  large  scale  (1:25,000) 
maps  of  various  countries  in  the  world  have  shown  that  it  is  pos- 
sible to  predict,  with  reasonable  accuracy,  the  probability  of  being 
able  to  see  continuously  for  a given  distance  from  a random  point 
within  the  area.10 

For  the  infantry  study,  the  procedure  used  in  the  map  analyses 
was  to  measure  the  continuous  ranges  of  visibility  between  infantry- 
men, with  the  position  of  one  man  (the  defender)  being  at  ground 
level  (foxhole  or  prone)  and  the  approaching  enemy  being  an  erect 
human  target  five  feet  high.  This  factor  was  chosen  to  set  realistic 
limits  on  the  range  of  iiit$r visibility  betwqen^opposing  forces.  The 

unclassified 


ORO-T-160 


11 


validity  of  the  map  readings  was  verified  by  actual  terrain  meas- 
urements* and  the  findings  are  in  general  agreement  with  limited 
combat  data  from  the  Korean  experience  and  ETO  experience  dur- 
ing World  War  II.** 

From  the  map  study,  it  was  found  that  all  the  types  of  terrain 
so  far  considered  fall  into  one  of  three  categories  which  are  illus- 


0 500  1000  1500 

R (YD) 


Fig*  2 — Frequency  distribution  for  ranges  of  continuous  visibility  for  Terrain  Classes 
A,  B,  and  C.  (Probability  of  seeing  man-targets  at  ranges  greater  than  R yards  from  a 
random  point  within  the  area  covered  by  the  map  analysis.) 


* Tests  were  conducted  on  the  battlefield  area  of  Gettysburg  in  which  a small  party  of 
ORO  analysts  checked  map  predictions  by  actually  walking  over  the  terrain  in  accord- 
ance with  the  map  bearings  and  measuring  the  distance  of  intervisibility.  In  every 
instance,  distances  of  continuous  visibility  were  found  to  be  less  than  the  distances 
predicted  by  map  measurement  because  of  terrain  features  and  obstacles  not  shown  on 
maps.  Map  readings  were  considered,  therefore,  to  represent  maxima. 

The  mean  ranges  of  visibility  from  map  analyses  of  Korea  and  Normandy  show  remark- 
able agreement  with  limited  combat  knowledge  of  ranges  of  engagement  between 
riflemen  and  between  tAnks.  In  Korea,  the  frequency  of  ranges  for  bullet  hits  agreed 
with  the  frequency  of  ranges  for  visibility.  For  World  War  II  tank  battles,  both  Peterson 
of  Ballistics  Research  Laboratory  and  ORO  (Ref.  10)  have  shown  that  ranges  of  engage- 
ment for  tanks  correspond  with  ranges  of  visibility  in  the  battle  areas  as  determined 
from  map  analysis.  These  two  samples  of  combat  data  tend  to  validate  the  use  of  the 
map  data  for  predicting  range  requirements. 


ORO-T-160 


* 


linin'*  SECRET- 


1 


sified 


trated  by  the  three  curves  in  Fig.  2.  The  frequency  distribution 
for  Type  A terrain  is  typical  for  a country  like  the  Saint-Lo  area 
in  Normandy,  where  visibility  is  sharply  limited  by  the  masses  of 
hedgerows,  small  cultivated  fields,  orchards,  and  the  nature  of 
the  terrain  itself.  Type  A also  describes  rugged,  mountainous 
terrain  like  Korea.  The  distribution  curve  for  Type  C describes 
relatively  open  country  where  the  topography  is  gently  rolling  and 
large,  open,  cultivated  areas  exist.  Type  B is  intermediate  between 
the  two  extremes  cited  and  describes  an  average  type  of  cultivated 
countryside. 

The  importance  of  these  data  to  the  infantry  study  is  related 
to  the  range  requirements  for  infantry  weapons  and,  as  shown  in 
Fig.  2,  95  percent  of  all  observations  include  ranges  which  are  much 
less  than  the  range  capabilities  of  many  of  the  infantry  direct  fire 
weapons.  The  implication  that  such  weapons  may  be  over -designed 
is  appreciated  when  it  is  considered  that  the  rifle  alone  has  a 
maximum  range  capability  of  3,500  yd. 

The  following  description  of  the  procedure  used  in  the  map  study 
is  presented  so  that  the  practical  application  of  the  data  may  be 
recognized. 

Figure  3 shows  diagrammatic  ally  a corner  section  of  a 1:25,000 
map.  The  method  of  measurement  was  adopted  from  a suggestion 
by  Peterson  of  Ballistics  Research  Laboratory  who  used  map  grid 
lines  as  guides  for  sampling  any  given  terrain. 

The  analysis  of  each  map  is  begun  at  Point  A (northwest  corner). 
Proceeding  along  the  east-west  grid  line,  the  distance  is  measured 
from  the  edge  of  the  map  to  the  point  where  an  erect  (five  feet) 
infantryman  would  just  be  obscured  from  the  sight  of  a defending 
prone  infantryman  at  Point  A.  In  this  case,  the  crest  of  a hill 
(contour)  is  the  factor  which  obstructs  visibility.  After  recording 
the  distance  A to  B,  the  next  point  of  obscuration  is  measured  by 
proceeding  along  the  grid  line  from  Point  B to  Point  C where  a 
railroad  embankment  interrupts  the  line  of  vision.  Distance  BC 
is  then  recorded  and  so  on  along  the  grid  line  to  the  far  edge  of 
the  map.  It  will  be  noted  that  a house  or  building  limits  visibility 
at  Point  D and  woods  limit  vision  at  Point  E. 

After  all  horizontal  grid  lines  are  measured  in  this  way,  the 
same  method  is  used  on  all  vertical  grid  lines.  Then  all  the  obscu- 
rations from  one  map  are  used  to  plot  a frequency  distribution. 
Examples  of  such  frequency  distribution  have  been  given  already 


in  Fig.  2. 


ORO-T-160 


13 


SfCftET 


1 ^ 
r j' 


Although  the  frequency  tlistri^utioh  curyes  yield  predictions  as 
to  the  probability  of  seeing  man  targets  at  Range  R,  from  any  ran- 
dom point  on  the  terrain,  it  may  be  argued  that  infantrymen  are 
not  randomly  located  along  the  front  but  actually  take  up  positions 
which  have  been  selected  for  point  of  advantage  (for  example,  high 
ground  in  the  defence).  So  far  as  this  is  true  for  small  units  such 
as  squads  and  platoons  especially  in  defensive  positions,  such  biases 
as  a result  of  the  placement  of  men  are  not  systematic,  and  when 
division  or  corps  fronts  are  considered,  the  density  of  men  and 
their  positions  across  a broad  front  can  be  considered  to  be  more 


Edge  of  Map 


Starting  at  the  northwest  corner  of  the  map  one  looks  from  the  point  A/  where  the  first  hori- 
zontal grid  line  begins,  along  that  grid  line  to  the  point  B where,  because  he  has  gone  over 
the  crest  of  a hill,  the  standing  infantryman  (the  target)  ceases  to  be  visible.  The  distance 
AB  is  measured  and  recorded.  Next,  starting  from  B,  one  finds  that  the  target  is  continu- 
ously visible  until  the  railroad  embankment  at  C causes  obstruction  to  view;  the  distance 
BC  is  then  measured  and  recorded.  Similarly,  starting  from  the  top  of  the  embankment,  it  is 
clear  that  there  is  no  obstacle  until  one  reaches  the  house  at  D;  CD  is  measured  and 
recorded.  Next  the  distance  DE  is  recorded;  then,  starting  from  the  eastern  edge  of  the 
wood,  the  distance  to  the  next  obstruction  is  measured;  and  so  on  across  the  map  to  the 
right  margin.  After  all  horizontal  grid  lines  have  been  followed  in  this  way,  one  starts 
again  at  the  northwest  corner  and  reads  from  F down  the  first  vertical  grid  line  and  all  the 
other  grid  lines.  All  the  readings  obtained  in  this  way  are  used  to  plot  a frequency  distri- 
bution. Figures  2 through  7 are  examples  of  such  frequency  distributions. 


14 


ORO-T-160 


or  less  uniform.  Thus,  in  relation  to  terrain,  their  position  is 
more  nearly  random.  Also,  no  systematic  selection  of  ground  is 
permitted  either  side  during  a battle,  since  position,  which  is 
fluid  and  constantly  changing,  is  dependent  upon  the  whole  battle 
situation  and  not  just  upon  ground  features.  Therefore,  the  random 
selection  on  a map  of  a battlefront  in  any  given  terrain  should  pre- 
dict the  actual  ground  condition  of  the  battlefield.  In  general,  it  is 
felt  that  men  move  in  battle  in  a more  or  less  random  manner,  so 
the  data  obtained  in  the  visibility  study  are  reasonably  valid  for 
predicting  the  probability  of  seeing  targets  over  any  area,  particu- 
larly since  the  method  used  measured  the  type  of  movement  used 
by  troops  in  battle,  that  is,  from  cover  to  cover. 

Employing  this  method,  map  studies  of  Canada,  France,  Germany, 
Korea,  North  Africa,  and  the  US,  to  a total  of  some  18,000  readings, 
showed  that  70  percent  of  the  ranges  at  which  an  erect  human  target 
can  be  seen  by  a defending  prone  rifleman  are  less  than  300  yd  (and 
that  90  percent  are  less  than  700  yd). 

Since  range  requirements  exert  a considerable  if  not  dominating 
influence  upon  such  characteristics  as  weight,  caliber,  and  missile 
velocity,  the  data  from  the  map  analyses  have  a very  important 
bearing  upon  the  design  of  an  infantry  hand  weapon.  Comparing  the 
range  analysis  data  with  the  maximum  range  of  the  present  M-l 
rifle  (3,500  yd),  and  its  design  for  incapacitating  clothed  personnel 
up  to  1,200  yd,  it  may  be  concluded  that  the  effective  ranges  of  the 
greater  part  of  infantry  hand  weapons  could  be  reduced  materially 
to  an  order  suggested  by  the  terrain  analysis.  (A  reduction  of  the 
range  of  the  rifle  for  maximum  effectiveness  up  to  300  yd  does  not 
mean  that  the  weapon  would  not  be  effective  at  ranges  beyond  this. ) 


THE  RIFLEMAN  AND  HIS  WEAPON 

Marksmanship:  Tests  and  Analyses 

The  preceding  sections  have  described,  to  some  extent,  certain 
major  factors  dictating  the  actual  operational  requirements  for  the 
general-purpose  hand  arm  of  infantry.  Since  marksmanship  obviously 
plays  a major  role  in  the  over -all  effectiveness  of  hand  weapons  em- 
ployment in  the  military  situation,  the  measure  of  the  varying  capa- 
bilities of  combatants  to  use  their  weapons  with  tactical  effectiveness 
becomes,  along  with  target  visibility,  a significant  parameter  in  the 
whole  infantry  study. 

To  provide  meaningful  data  on  this  subject,  field  tests  were  con- 
ducted at  Fort  Belvoir,  Virginia,  where  16  expert  riflemen  (highest 


ORO-T-160 


15 


grade)  and  16  marksmen  (lowest  qualified  grade)  were  used  in  a 


series  of  experiments  designed  to  simulate  some  of  the  conditions 
of  combat.  The  32  men  were  divided  into  groups  for  two  sets  of 
tests.  Firing  the  M-l  rifle  from  the  prone  position,  using  battle 
sights,  they  shot  at  a man- silhouette  target  operated  on  a tran- 
sition-type range,  at  distances  of  100-300  yd.  Mounted  behind  the 
silhouette  was  a 6 foot  high  by  12  foot  wide  screen;  on  this  could  be 
measured  the  dispersion  of  rounds.  The  target  butts  were  draped 
with  OD  cloth  so  that  short  rounds,  not  striking  the  target,  could 
also  be  recorded.  (These  experiments  and  the  results  are  described 
in  detail  in  the  Appendix.  ) 

Further  data  were  procured  from  a range  test  on  automatic 
rifles  at  Fort  Benning,  Georgia.* 

In  the  tests  at  Belvoir,  a variety  of  conditions  was  imposed  on 
the  participants  chiefly  by  changing  the  time  of  target  exposure 
and  imposing  forms  of  psychological  duress.  It  was  found  that 
best  results  were  obtained  when  single  rounds  were  fired  on  an 
individual  basis  at-sfatic  man-size  targets.  Marksmanship 
declined  when  group  firing  (4-man  groups)  was  performed  at  the 
same  targets.  With  slight  psychological  load,  in  the  form  of 
limited  target  exposure  time  and  random  order  of  presentation 
at  varying  ranges,  a further  decline  in  effectiveness  was  noted. 

Hit  probability  as  a function  of  range  for  both  grades  of  riflemen 
is  shown  in  Fig.  A4  (Appendix). 

Significant  results  from  these  analyses  are:  (a)  hit  probability 
is  high  for  both  grades  of  riflemen  at  ranges  up  to  100  yd;  (b)  at 
ranges  beyond  100  yd,  a sharp  decline  in  hit  probability  occurs 
and  this  decline  in  effectiveness  is  most  marked  at  the  common 
battle  ranges,  between  100  and  300  yd;  (c)  at  500  yd,  both  experts 
and  marksmen  perform  unsatisfactorily,  a performance  quite 
inconsistent  with  the  design  capability  of  the  weapon  and  with 
military  specifications.** 

These  findings  provide  part  of  the  explanation  for  most  fre- 
quent battle  use  of  rifles  at  ranges  less  than  300  yd  and  for  the 

The  author  acknowledges  the  assistance  of  Lt  Col  D,  E,  Munson  of  ORO  in  arranging 
for  these  tests  and  in  helping  with  test  designs  which  were  in  keeping  with  the 
practical  aspects  of  conditions  of  combat. 

**For  the  issue  M-l  rifle  and  standard  M-2  ammunition,  the  mean  radial  dispersion  is  about 
ten  inches  at  a range  of  500  yd.  An  indication  of  the  discrepancy  existing  between  the 
inherent  accuracy  of  the  weapon  and  ammunition,  on  the  one  hand,  and  that  of  the  man- 
rifle  combination,  on  the  other,  may  be  found  by  comparing  miss  probabilities  at  the 
range  of  greatest  interest,  namely  300  yd.  In  a machine  or  bench  rest,  the  probability 
that  the  rifle- ammunition  combination  will  miss  the  type  E silhouette  target  (which 
approximates  the  head  and  torso  region  of  an  erect  human  target — projected  area  about 
4.6  sq  ft)  at  300  yd  is  about  PM  = .040;  whereas,  for  marksmen  firing  individually,  the 
probability  of  a miss  is  Pm  - 0.76. 


16 


ORO-T-160 


IHIPUMMtm 


incurrence  of  the  majority  of  rifle  bullet  wounds  in  combat  within 
this  range.  Since  deflection  errors  in  aiming  are  independent  of 
range  (Appendix),  the  sharp  decrease  in  hits  beyond  100  yd  is  not 
to  be  attributed  to  men  becoming  less  accurate  at  the  longer  ranges 
the  hit  probabilities  shown  by  the  curves  are  a function  of  target 
size  and  range. 


A Experts  individually  firing  new  weapon 
B Experts  firing  individually 
C Marksmen  firing  individually 
D Marksmen  firing  simultaneously 

Fig.  4 — Marksmanship  using  the  M-l  Rifle 

(Probability  of  hitting  target  as  function  of  range) 


The  difference  between  expert  riflemen  and  marksmen, 
although  significant  at  some  ranges  in  these  tests,  may  or  may 
not  be  meaningful  in  actual  combat  where  man  targets  will  be  in 
movement  and  psychological  duress  will  be  high.  In  fact,  in  the 
rapid  fire  tests  using  targets  randomly  presented  (see  Appendix, 
Test  3),  the  marksmanship  of  experts  declined  significantly  when 
compared  to  simultaneous  firing  in  Tests  1 and  2.  The  same 
comparison  for  marksmen  showed  that  the  rapid  fire  test  did  not 
significantly  affect  their  performance,  indicating,  perhaps. 


ORO-T-160 


17 


that  under  the  rigorous  conditions  of  combat,  only  slight  differ- 
ences exist  in  marksmanship  among  the  several  qualifications  as 
determined  on  the  range. 

In  a fire  fight,  it  is  reasonably  certain  that  marksmanship 
will  be  less  effective  than  shown  by  the  curves  in  the  tests  which, 
for  this  reason,  are  presumed  to  be  optimistic  as  relating  to  the 
actual  situation. 

In  connection  with  the  dispersion  inherent  in  the  weapon  and 
in  the  ammunition  used,  it  is  interesting  to  note  that,  at  all  com- 
mon ranges,  weapon  errors  are  without  significance  in  the  man- 
weapons  system.  As  already  pointed  out,  considerable  discrepancy 
exists  between  the  accuracy  of  the  weapon  and  that  of  the  riflemen. 
In  the  Appendix,  it  is  shown  that  the -dispersion  of  the  weapon  could 
be  more  than  doubled  without  materially  affecting  the  probability 
of  hitting  the  target.  As  shown  in  Fig.  A43,  weapons -design 
standards  which  seek  perfection  by  making  the  rifle  more  accurate 
(approach  zero  dispersion)  would  not  be  reflected  in  improved 
marksmanship  or  musketry.  Such  high  standards  of  precision  and 
accuracy  on  the  part  of  present  designers  are  not  supported  by 
this  analysis  as  genuine  military  requirements.  Results  of 
the  analysis  on  marksmanship  were  also  used  to  predict  the  value 
of  using  a weapon  which  would  tend  to  compensate  for  man-aiming 
errors  by  firing  a pattern  salvo,  or  volley.*  In  Fig.  4,  one  of 
the  examples  of  hit  effectiveness  for  such  a weapon  is  presented 
(from  the  Appendix). 

The  Pattern  Salvo  Weapon 

As  shown  by  field  test,  errors  in  aiming  have  been  found  to  be 
the  greatest  single  factor  contributing  to  the  lack  of  effectiveness 
of  the  man-rifle  system.  In  particular,  the  men  who  are  graded 
by  Army  standards  as  expert  riflemen  do  not  perform  satisfactorily 
at  common  battle  ranges,  a fact  which  casts  grave  doubt  on  any 

The  results  of  the  tests  on  marksmanship  already  have  astonished  many  persons 
because  it  was  not  expected  that  men  would  exhibit  such  low  performance  at  the 
common  ranges.  The  factors  which  possibly  explain  the  disparity  between  the  higher 
marksmanship  scores  from  Army  training  methods,  when  firing  on  known  distance 
ranges,  and  the  lower  scores  from  the  ORO  tests  are  apparently  connected  with  the 
conditions  of  the  tests  which  neither  simulated  Army  methods  of  scoring  or  approached 
the  true  conditions  of  combat.  Perhaps  by  adopting  training  methods  along  the  lines  of 
the  tests  conducted,  the  performance  of  men  might  show  some  general  improvement.  In 
any  case,  the  test  results  are  believed  to  be  more  indicative  of  the  actual  capabilities 
of  riflemen  in  a military  situation  than  the  qualification  score  made  when  firing  for 
record  on  the  range.  The  ORO  test  data  already  have  been  used  in  other  analyses 
relating  to  the  weapons  system  and  have  proven  of  great  value.  Because  they  may  prove 
useful  to  other  workers  in  military  analysis,  the  Appendix  has  been  written  to  include 
most  of  the  raw  data  in  the  form  of  tables  and  figures,  resulting  in  “bulk”  for  which 
there  is  no  other  warrant. 


ORO -T- 160 


g*"11 11 'SECRET 


attempt  at  the  development  of  skills  through  training  which  would 
begin  to  approach  the  accuracy  of  the  weapon  itself.  Although  care- 
ful selection  and  intensive  training  of  personnel  in  the  use  of  the 
rifle  may  accomplish  much  in  improving  marksmanship  in  peace 
time,  the  problems  of  rapid  Army  expansion  and  accelerated  train- 
ing in  time  of  national  mobilization  preclude  the  opportunity  to 
develop  highly  skilled  riflemen  in  large  numbers  by  selection  or 
through  prolonged  training.  This  point  is  often  overlooked  by  those 
who  argue  for  better  training  as  the  only  solution  for  the  rifle  pro- 
blem. Actually,  to  reach  truly  proficient  standards  in  marksman- 
ship, the  time  required  in  training  would  greatly  exceed  the  prac- 
tical limits  imposed  on  Army  training  schedules  by  the  needs  of 
mobilization.* 

In  the  search  for  alternatives  to  an  extensive  (and  impracticable) 
training  program,  consideration  was  given  to  the  possibility  of 
compensating  for  man-aiming  errors  through  a weapon-design 
principle.  The  results  of  the  marksmanship  study  indicate  that  a 
cyclic  or  salvo-type  automatic  fire  arm  offers  promise  of  increasing 
hit  effectiveness  if  the  missiles  in  a burst  or  salvo  were  projected 
so  as  to  be  dispersed  randomly  or  uniformly  around  the  point  of 
aim.  Obviously,  a uniform  type  of  dispersion  would  be  more 
desirable  than  random  dispersion  if  hit  effectiveness  were  to  be 
maximized.  In  considering  such  a weapon,  two  points  required 
determination:  (a)  a practical  limit  on  the  number  of  rounds  per 
burst  or  volley;  and  (b)  the  pattern  design  of  the  rounds  to  be 
delivered. 

In  the  Appendix,  the  consideration  of  four-  and  five -round 
salvos  was  not  arbitrary.  Wound  ballistics  data  show  that  small 
caliber  missiles  of  high  velocity  could  be  used  in  the  new  weapon 
(see  section  on  Wound  Ballistics),  which  suggested  the  possibility 
of  obtaining  logistic  equivalence  (that  is,  equivalence  in  weight  of 
weapon  and  ammunition  carried)  between  a four -round  salvo  and 
present  single-shot  rifle  fire**;  also,  not  less  than  four  rounds 
would  be  required  to  form  a symmetrical  pattern  (diamond- shaped) 

One  expert  rifleman  at  Fort  Be nning,  Georgia , estimated  that  it  required  nine  years  of 
continuous  training  on  fire  arms  to  develop  marksmanship  to  the  proficient  level  which 
he  now  enjoys.  Sgt.  Justice’s  performance  in  demonstrating  the  use  of  infantry  hand 
weapons  is  most  dramatic.  His  skill  in  marksmanship  actually  approaches  the  accuracy 
of  the  weapon;  he  has  attained  a level  of  performance  roughly  commensurate  with  the 
design  precision  of  the  weapon.  However,  it  is  estimated  that  less  than  10  percent  of 
the  men  in  the  normal  recruit  stream  could  possibly  reach  this  level  of  small  arms 
proficiency,  even  if  time  allowed  for  training  were  long. 

* * 

Calculations  actually  reveal  that,  for  a high  velocity,  .21  cal  missile  of  60  grains,  the 
ratio  of  cartridge  weights  for  M-l  standard  ball  ammunition  and  the  small  caliber  rounds 
would  be  about  1.6 : 1. 


ORO-T-160  19 


around  the  point  of  aim  which  would  tend  to  maximize  hit  prob- 


ability on  the  human-target  shape.* 

As  shown  in  the  Appendix,  a cyclic  or  salvo-type  hand  weapon 
would  materially  increase  the  effectiveness  of  aimed  fire  among 
the  infantry.  Although  not  all  possibilities  in  pattern  dispersions 
and  numbers  of  rounds  were  analyzed,  it  appears  that  the  best 
design  (for  the  greatest  practical  gains)  is  one  using  the  four- 
round  salvo  with  20  in.  spacing  among  rounds  at  300  yd  range. 
The  development  of  a salvo  weapon  having  these  characteristics 
represents  an  ideal  toward  which  effort  might  be  directed;  it  is 
not  suggested  that  this  is  the  only  solution. 

By  considering  the  need  to  maintain  minimal  logistic  require- 
ments (number  of  rounds)  and  minimum  weight,  a weapon  which 
conformed  to  the  principle  of  this  design  would  tend  to  optimize 
the  military  effects  of  a fire  arm,  per  se.  To  add  to  these  gains 
materially,  an  impractical  number  of  rounds  per  salvo  or 
burst,  or  an  entirely  different  weapon  would  be  required** 

From  the  analysis  of  the  dispersion  of  shots  fired  at  various 
ranges,  it  was  possible  to  calculate  the  relative  effectiveness  of 
a hypothetical  new  type,  salvo  automatic  weapon,  which  was 
assumed  to  differ  from  the  M-l  rifle  only  in  the  manner  in  which 
the  missiles  were  projected.  Examples  of  the  effectiveness  of 
four-  and  five-round  salvos  with  20  in.  spacing  among  rounds  at 
varying  ranges  are  given  in  Figs.  A41  and  A42.  It  will  be  noted 
that  a four-round  salvo  of  20  in.  spacing  at  300  yd  would  more 
than  double  hit  effectiveness  at  this  distance.  Coincidentally, 
this  increase,  through  a design  change  alone,  would  raise  the 
performance  of  common  marksmen  using  the  salvo  weapon  to  the 
level  of  expert  riflemen  using  the  M-l. 

From  this  analysis  of  marksmanship  and  its  relation  to  a 
given  weapon,  it  is  concluded  that:  (a)  The  marked  decrease  in 

*The  analysis  (Appendix)  suggests  that  the  human  target  is  represented  reasonably  well 
by  a circular  shaped  target.  Since  the  average  projected  area  of  the  body  in  combat  is 
less  than  2 sq  ft*  and  a man  is  about  20  in.  wide,  the  average  human  target  is  thus  more 
nearly  represented  by  a rectangle  approximately  12  in.  X 20  in.  if  the  profile  of  the 
head  on  the  shoulders  were  not  considered.  Considering  the  head,  however,  the  average 
human  target  in  combat  does  approximate  a circle. 

A hand  weapon  could  be  designed  like  a Very  pistol  and  project  small  fragmentation 
shells  which  could  be  directed  at  the  enemy  in  much  the  same  way  as  grenades.  By 
using  the  new  principle  of  controlled  fragmentation  shells  and  employing  some  unique 
time  fuze,  it  might  be  possible  to  reach  a level  of  true  maximum  effects  for  fire  arms. 
The  problem  would  be  connected  with  the  fuze  and  not  the  launcher  if  missile  bursts 
were  to  be  controlled  over  the  heads  of  the  enemy.  Such  a weapon  would  require 
considerable  technical  development,  involving,  probably,  a longer  range  program  than 
a pattern-dispersion-type  fire  arm.  Any  contemplated  plan  for  proceeding  with  the 
development  of  fragmentation  hand  arms  should  cause  the  dispersion  weapon  to  be  an 
intermediate  step  in  the  developmental  chain. 


20 


ORO-T-160 


1 


INFORMATION 

C 

* it*  o H 

ifey 


hit  probability  occurring  between  100  and  300  yd  suggests  that 
significant  improvement  in  effectiveness  at  these  ranges  cannot 
be  achieved  by  increasing  the  ballistic  accuracy  of  the  weapon: 
aiming  errors  are  too  great  to  be  compensated  by  any  improve- 
ment in  the  accuracy  of  the  rifle  alone,  (b)  A cyclic  or  salvo 
automatic  weapon  could  compensate  largely  for  these  aiming 
errors  if  the  missiles  were  projected  with  a dispersion  pattern 
designed  to  maximize  the  probability  of  a hit  on  the  human  target 
at  ranges  which  most  frequently  recur  in  combat  (up  to  300  yd). 


Full -Automatic  Fire 

The  last  conclusion  prompted  an  examination  of  the  opera- 
tional performance  of  current  models  of  fully  automatic  rifles 
to  determine  whether  these  desirable  characteristics  obtained. 
Two  questions  were  salient:  (a)  As  the  fully  automatic  rifle  is 
ordinarily  aimed  and  fired,  what  is  the  nature  of  the  shot  dis- 
persion from  short  bursts?  (b)  Does  automatic  fire  in  short 
bursts  increase  the  probability  of  a hit  on  a man-size  target, 
especially  at  ranges  of  100  to  300  yd? 

To  answer  these  questions,  tests  were  arranged  at  Fort 
Benning,  Georgia,  in  which  both  expert  riflemen  and  marksmen 
used  current  models  of  full  automatic  rifles.  Type  E silhouette 
targets  were  mounted  in  front  of  six  by  six-ft  target  screens. 
The  first  firing  serial  was  at  100  yd  using  controlled  bursts  of 
five  rounds  each.  Never  did  more  than  one  round  hit  the  target 
or  screen  from  any  of  the  short  bursts,  and  consequently  no 
information  could  be  obtained  at  100  yd  on  the  nature  of  the 
dispersion  pattern.  To  obtain  more  than  one  strike  on  the  six 
by  six-ft  screen,  the  range  had  to  be  closed  to  50  yd.  At  this 
short  range  it  was  noted  that  the  man- silhouette  target  in  front 
of  the  screen  was  not'  hit  more  than  once  from  any  burst.  Since 
single  round  firing  with  the  M-l  rifle  at  50  yd  yields  a proba- 
bility of  hit  of  near  unity,  the  effectiveness  of  automatic  fire 
at  such  short  ranges  was  of  no  interest. 

The  results  of  these  trials  (although  preliminary)  strongly 
suggested  that  the  emphasis  and  impetus  currently  being  placed 
by  the  US  and  other  NATO  countries  on  the  development  of  fully 
automatic  hand  weapons  should  be  questioned  on  the  basis  of 
actual  military  requirements  for  the  automatic  feature.  ORO 
plans  to  make  further  tests*  of  infantry  weapons  and  some  of 
these  tests  will  include  further  work  on  shot  dispersions  of 


It  is  planned  to  :stablif 


ORO-T-160 


tactical  research  laboratory  at  Fort  Benning,  Georgia. 


21 


5E' 


infantry  hand  arms.  However,  any  work  bearing  on  the  estab- 
lishment of  military  requirements  for  weapons,  especially 
automatic  hand  arms,  should  provide  operational  data  upon 
which  decisions  can  be  made.  In  this  connection,  it  might  be 
pointed  out  that  the  tests  on  automatic  rifles  conducted  at  Fort 
Benning,  Georgia,  do  not  constitute  the  type  of  weapons  eval- 
uation from  which  such  requirements  can  be  established.  In 
the  reports  of  these  tests,11  the  weakness  of  automatics  from 
an  operational  effectiveness  standpoint  was  not  revealed,  and 
it  is  unfortunate  that  such  large-scale  trials  should  not  have 
been  designed  scientifically  to  produce  data  upon  which  such 
facts  might  be  determined.  Any  comparison  of  automatic  and 
semiautomatic  weapons  should  be  designed  to  determine  military 
effectiveness  by  relating  hit  effectiveness  with  fire  power,  to 
include  rate  of  expenditure. 

From  the  preliminary,  yet  informative,  tests  conducted  by 
ORO  on  automatic  hand  arms  it  may  be  stated  that: 

1.  Regardless  of  the  skill  of  the  rifleman,  only  the  first 
round  in  a short,  fully  automatic  burst  can  actually  be  directed 
at  a point  target. 

2.  At  normal  battle  ranges,  all  shots  after  the  first  fall  off 
a man- size  target  in  an  approximately  linear  pattern,  the  pro- 
gressively greater  departures*  depending  in  magnitude  upon 
the  characteristics  of  the  weapon  and  the  manner  in  which  it  is 
held. 

3.  At  all  common  battle  ranges,  with  present  hand-held 
automatics,  the  strike  dispersion  is  so  great  that  moving  the 
center  of  impact  for  the  burst  to  the  center  of  the  target  would 
not  increase  the  number  of  hits. 

4.  Even  at  much  reduced  ranges,  where  more  than  one  hit 
from  a short  burst  is  scored  on  a man-size  target,  the  use  of 
a burst  can  be  justified  only  in  a limited  sense,  since  at 
these  ranges  single  rounds  (semiautomatic)  have  a probability 
of  near  unity  of  striking  the  target.  It  follows  that  reducing  the 
range  does  not  increase  the  probability  of  hitting  with  automatic 
fire,**  but  only  of  obtaining  multiple  hits,  Moreover,  when  at 
ranges  of  50  yd  or  less,  multiple  hits  become  probable,  the 

*The  rifleman,  by  a more  or  less  difficult  compensating  effort,  may  exert  a type  of 
control.  Such  control  is  in  itself  erratic  and  is  not  noticeable  before  5-10  rounds 
have  been  fired,  according  to  the  cyclic  rate  of  the  weapon. 

*This  result  is  inconsistent  with  current  rifle  design,  which  provides  a high  rate  of  fire 
in  an  effort  to  increase  the  number  of  targets  hit,  as  compared  with,  say,  the  model  1903 
rifle.  Thus,  automatic  fire  is  not  to  be  justified  oil  the  basis  of  an  increased  proba- 
bility of  obtaining  &hit  on  separated  man-size  targets. 


22 


ORCUT-160 


ry 


f 


ire 

.903 


160 


lethality  of  the  burst  increases  much  more  slowly  than  does  the 
number  of  hits  (see  section  on  lethality). 

5.  The  full  automatic  feature  of  current  infantry  weapons  is 
valueless  from  the  standpoint  of  increasing  the  number  of  targets 
hit  when  aiming  at  separated  man- size  targets.* 

Wound  Ballistics:  Missile  Caliber,  Mass,  and  Velocity 

Wound  ballisticians  have  recently  determined  that  the  "wound- 
ing power"  or  damage  capability  of  a missile  is  more  nearly 
proportional  to  the  cube  of  the  velocity  than  the  square.12  A 
reasonable  (and  acceptable)  measure  for  wound  severity  is  the 
maximum  volume  of  the  temporary  cavity  produced  in  the  tissue 
by  a penetrating  missile.  It  has  been  found,  for  example,  that 
the  effect  of  increasing  the  velocity  of  a small  caliber  missile 
more  than  compensates  for  the  reduced  mass.  Recent  work11 
has  shown  that,  if  extreme  ranges  are  not  important,  a smaller 
caliber  bullet  than  the  present  .30  cal  US  military  standard 
might  well  be  used.  Moreover,  evidence  shows  that  at  common 
ranges,  .22  cal  bullets  can  produce  wounds  of  measurably 
greater  severity  than  .30  cal  bullets  striking  with  the  same 
velocity,  providing  these  velocities  at  target  are  greater  than 
a certain  critical  value. 

Although  more  extensive  work  will  be  required  in  inves- 
tigating the  effects  of  nose  shape,  weight,  and  other  factors  as 
they  affect  flight  characteristics  and  wounding  ability,  it  has 
been  established  that  smaller  bullets  can  be  used  to  produce 
battlefield  physiological  effects  at  least  equivalent  to  those  of 
the  present  standard  .30  cal.  Substantial  logistics  savings  would 
also  accrue  from  the  introduction  of  substantially  lighter  and 
less  expensive  cartridges,  although  actual  savings  cannot  be 
expressed  quantitatively  until  further  research  indicates  the 
most  practical  weight  and  shape  of  bullet  to  employ.  The  areas 
of  incomplete  research  should  be  investigated  at  the  Biophysics 
laboratory,  the  Army  Medical  Center,  Edgewood,  Maryland, 
where  facilities  and  skilled  personnel  offer  the  opportunity  to 
advance  knowledge  in  this  field  in  a reasonable  length  of  time 
and  in  an  important  way. 

* 

During  the  course  of  this  study,  the  author  considered  the  various  possible  uses  of 
present  automatics  in  combat  where  the  automatic  feature  (and  the  wide  dispersion  of 
rounds)  would  be  militarily  useful.  Discussion  with  experienced  infantry  combat 
commanders  and  other  military  specialists  led  to  the  conclusion  that  although  the 
feature  was  useful  in  tight,  close-in  positions,  usually  another  weapon  (e.g.,  a grenade) 
could  be  used  to  greater  advantage  than  could  a burst  from  an  automatic.  Also,  it  was 
indicated  that,  for  the  average  rifleman,  such  occasions  were  rare  and  did  not  consti- 
tute a basis  for  justifying  the  feature. 


ORO-T-160 


Quite  apart  from  the  idealized  concept  of  a salvo  weapon, 
sufficient  evidence  is  at  hand  to  be  quite  certain  that  a light, 
high-velocity,  small  caliber  rifle  could  be  designed  for  military 
use  and  could  fulfill  effectively  the  role  of  a general  purpose, 
lightweight  hand  arm. 

In  a recent  study14  conducted  by  D.L.  Hall  of  the  Terminal 
Ballistics  Laboratory,  Aberdeen  Proving  Ground,  a theoretical 
comparison  of  the  effects  and  military  usefulness  of  various 
calibers  of  rifles  shows  that,  when  the  combined  weight  of  wea- 
pon and  ammunition  is  held  constant  to  15  lb,  the  over-all 
expected  number  of  kills  for  the  .21  cal  rifle  is  approximately 
2.5  times  that  of  the  present  standard  .30  cal  rifle.  When 
compared  to  M-l  ammunition,  a .21  cal  missile  of  high  velocity 
(about  3500  feet  per  second  muzzle  velocity)  creates  equal  or 
greater  damage  than  the  standard  .30  cal  missiles  at  ranges 
up  to  800  yd.  This  evidence,  combined  with  the  work  of  Proj- 
ect BALANCE  (ORO)  on  ranges  of  visibility,  marksmanship, 
and  actual  operational  needs,  lends  considerable  support  to 
the  major  conclusion  that  lighter  hand  weapons  of  smaller 
caliber  may  well  be  provided  without  losing  military  effec- 
tiveness, while  offering  both  impressive  logistical  gains  and 
improved  operations. 

In  addition  to  these  gains,  the  advantages  of  low -recoil 
effects  offered  by  the  smaller  caliber  weapons  would  be  reflected 
in  improved  skill  in  the  use  of  the  weapon  by  allowing  a higher 
rate  of  single -round  aimed  fire.  Such  weapons  would  also  be 
much  less  fatiguing  to  handle.  Since  recoil  of  a small  caliber 
weapon  would  be  less  than  that  of  present  weapons,  the  disper- 
sion of  rounds  in  a short,  fully  automatic,  burst  could  be 
considerably  less  than  the  dispersion  of  current  models.  This 
important  characteristic,  yet  to  be  determined  by  actual  trial 
of  small  caliber  automatics,  might  possibly  be  the  most  prac- 
tical solution  to  the  problem  of  developing  an  automatic  fire 
arm  which  will  project  missiles  in  a burst  such  that  the  dis- 
persion of  rounds,  at  ranges  up  to  300  yd,  would  approach  the 
ideal  dispersion  for  maximum  effects  as  indicated  in  the 
Appendix. 

The  studies  and  experimental  development  work*  currently 
being  undertaken  by  the  Ordnance  Corps  at  Aberdeen  Proving 

Discussion  with  G.  A.  Gufstafson  of  the  Small  Arms  Section  of  BRL  indicated  that  it  is 
feasible  to  design  small  caliber,  high  velocity,  automatic  rifles,  which  would  exhibit 
short-burst  dispersion  patterns  at  ranges  up  to  300  yd,  tending  to  approach 
dimensionally  the  ideal  patterns  outlined  in  the  Appendix. 


24 


ORO-T-160 


SB 


LATION 


PWTORMATION 


1 ! 

U 


\ 


I * \ 


&ddlifo 


Ground  should  be  encouraged  to  proceed  toward  a rifle  develop- 
ment which  will  fulfill  these  important  military  characteristics. 
Although  such  a light  weapon  would  not  compensate  for  human 
aiming  errors  when  fired  semiautomatically,  it  is  quite  possible 
that  automatic  fire  in  short  bursts  at  common  battle  ranges 
would  produce  dispersion  patterns  commensurate  with  the 
requirements  of  the  idealized  salvo  weapon.  In  particular,  the 
low  recoil  of  a small  caliber  rifle  offers  the  chance  to  employ 
a muzzle  compensator  with  significant  effects,  lending  added 
promise  to  a satisfactory  development.  If  the  development  of 
this  light,  high  velocity  weapon  could  proceed  to  include  the 
ideal  salvo  principle,  obviously  a truly  effective  hand  arm 
could  be  provided. 


LETHALITY 


Weapons  in  General 

The  history  of  the  development  of  weapons  and  tactics  shows 
an  interesting  process  of  self -adjustment.  It  has  been  found, 
from  an  examination  of  many  campaigns  from  Marathon  to 
Korea,  that  battles  are  no  more  bloody  now,  despite  vastly 
"improved"  weapons,  than  they  were  in  the  days  of  the  short 
sword:  the  casualties  incurred  per  number  of  men 

engaged  per  unit  of  time  remains  about  constant.*  In  fact, 
it  may  well  be  that  the  sword  is  much  more  lethal  than  con- 
ventional weapons  because  it  can  be  directed  with  more 
control  at  the  vulnerable  areas.lt  remains  to  be  seen  whether  the 
tactical  use  of  atomic  and  new  CBR  weapons  will  alter  this 
trend. 

The  explanation  for  this  apparent  constancy  in  the  intensity 
of  battle  effects  seems  to  be  related  to  the  compensating 
changes  in  tactics  which  each  new  weapon  introduces.  Most 
advances  in  weapons  either  increase  the  distance  over  which 
a blow  can  be  delivered  (improved  launcher)  or  increase  the 
lethal  radius  or  radius  of  effect  (improved  missile),  or  both. 

The  ratio  of  the  lethal  area  to  the  concentration  (or  density) 
of  enemy  targets  appears  to  have  remained  constant.  Since 
logistics  costs  have  markedly  increased  since  the  early  wars, 
war  itself  has  become  vastly  more  costly  in  terms  of  the 
effect-cost  ratio,  yet  little  if  any  more  effective  in  terms  of 
personnel  casualties  per  unit  time  or  per  unit  effort. 


From  an  unpublished  ORO  study. 


| W'  ' 

f A f Q l t* ir  * o.  a 


ION 


ORO-T-160 


25 


Although  these  are  measures  of  gross  intensity  for  war 
(total  casualties  only),  it  is  interesting  to  note  that  severity 
of  weapons  as  measured  by  their  lethality  has  not  changed, 
at  least  in  the  past  century.  If  the  lethal  indices  of  weapons 
(also  a constant)  could  be  raised,  efficiency  and  effect  might 
well  be  improved  materially,  and  no  compensating  tactical 
adjustment  would  be  practicable.  It  is  believed  that  the 
means  for  doing  this  are  at  hand,  and,  with  special  reference 
to  one  weapon  (the  infantry  hand  arm),  an  estimate  is  made 
in  a following  section  of  expected  results  if  bullet  lethality 
were  increased,  as  seems  technologically  feasible. 

The  Rifle 

The  lethal  index  of  a weapon  corresponds  roughly  with 
tactical  effectiveness  since  it  refers  to  those  wounds  which 
are  speedily  lethal,  the  condition  of  which  cannot  be  reversed 
by  medical  intervention.  Since,  by  this  definition,  "lethal1' 
effects  result  in  death  very  quickly  (or  death  is  assured), 
the  lethal  index  is  a measure  of  tactical  effect.  Therefore, 
in  the  forward  areas  of  the  combat  zone,  where  bitter  hand- 
to-hand  fighting  occurs,  there  is  no  sound  basis  for  arguing 
against  the  merit  of  disposing  of  the  enemy  in  the  shortest 
possible  time  by  inflicting  maximum  physical  trauma.  For 
the  infantry  hand  arm,  the  infliction  of  severe  wouifds, that 
are  immediately  incapacitating,  is  important. 

As  stated  earlier,  the  lethal  index  of  the  rifle  exceeds 
30  percent  when  hits  at  all  ranges  are  considered,  and, 
with  the  exception  of  the  machine  gun,  it  is  the  most  lethal 
weapon  of  all  conventional  missile  projecting  ground  arms. 

Comparison  of  Lethality  of  an 

Ideal  Dispersion  Automatic  with  M- 1 Single -Shot  Fire 

From  Table  A9  and  Fig.  A40  in  the  Appendix,  it  is  pos- 
sible to  estimate  the  lethality  of  an  ideal  dispersion  weapon 
at  the  various  battle  ranges  and  compare  these  effects  with 
those  of  the  rifle.  Because  no  exact  information  exists 
concerning  the  vital  area  complex  of  the  body  or  the  effects 
on  lethality  of  multiple  hits,  it  was  necessary  to  assume  that 
all  bullets  from  a salvo,  or  burst,  are  independently  lethal 
and  that  multiple  hits  are  incurred  at  random  relative  to  the 
vulnerable  areas.  Obviously,  this  assumption  ignores  the 
fact  that  physiological  effects  of  multiple  wounds  are  cumu- 
lative (shock,  exsanguination,  and  the  like),  and  that  hits 


26 


ORO  -T  -160 


e 


1 


4 


^ if*'  o 

Ifjj  i j • J 


from  the  ideal  dispersion  weapon  follow  a pattern  design  and 
do  not,  therefore,  strike  at  random.  Since  cumulative  effects 
of  multiple  wounds  add  to  lethality,  and  since  any  lack  of 
randomness  in  the  hits  may  or  may  not  favor  the  probability 
of  striking  mortally  vulnerable  areas,  the  estimates  given  may 
be  strengthened  perhaps  by  the  compensating  effects  of  these 
two  indeterminate  factors.  For  each  weapon,  is  assumed 
that  the  lethal  probability  of  a bullet  hit  is  O.3.* 

From  Table  A9  (Appendix]^ the  lethality  for  the  dispersion 
weapon  (five -round  salvo  pattern)  can  be  estimated  for  each 
category  of  single  and  multiple  hits  for  each  range.  An 
example  of  the  method  used  is  given  for  a range  200  yd: 
Probability  of  kill  per  bullet  hit,  PI  = 0.3; 

Probability  of  not  killing  per  hit,  Ps  = 0.7. 


Thus,  for  each  category  of  possible  hits  from  a five-round  salvo: 


Hits 

Ps 

PI 

1 

0.700 

0.300 

2 

0.490 

0.510 

3 

0.343 

0.657 

4 

0.240 

0.760 

5 

0.168 

0.832 

For  range  200  yd  (Table  A9),  the  probabilities  of  obtaining 
exactly  1,  2,  3,  4,  and  5 hits  with  the  five -shot  patterns  are: 


Hits 

1 

2 

3 

4 

5 

Ph** 

0.388 

0.122 

0.284 

0.0580 

0.000 

therefore, 

PhxPl  = 0.116  0.0622  0.187  0.0441  0.000 


At  range  200  yd,  the  probability  of  killing  an  enemy  per 
burst  is  the  sum  of  the  lethal  probabilities  = 0.409. 

For  single  rounds  from  the  M-l  rifle  at  200  yd,  the  kill 
probability  is  0.135  (Ph  = 0.45  and  PL  = 0.3,  Fig.  A40).  In 


The  lethal  index  of  the  rifle  bullet  exceeds  30  percent.  It  is  assumed  that  the  smaller 
caliber  bullet  for  the  new  weapon  would  be  equally  lethal  since  it  will  have  a wounding 
capability  equal  to  or  greater  than  the  M-l  at  the  ranges  involved. 

The  variations  noted  in  the  probabilities  for  obtaining  more  than  one  hit  are  due  to  the 
shape  of  the  human  target  as  it  affects  a strike  of  two  or  more  hits  from  the  dispersion 
pattern. 


f fnnfn 

_ « 

(J  1 [LI  H 

1 i | 

* K + t 

-160 


ORO-T-160 


27 


TION 


this  way,  the  lethality  of  the  two  weapons  may  be  compared 
as  shown  in  Fig.  5. 

The  curves  giving  the  lowest  lethal  limit*  and  the  prob- 
able upper  limit  for  the  dispersion  weapon  show  that  a 
considerable  relative  increase  in  lethality  over  the  rifle  may 
be  expected  through  the  use  of  the  dispersion  weapon  for 
ranges  beyond  100  yd.  The  theoretical  upper  limit  would 


x 


H- 

LU 

_J 

LL 

O 

>- 


CD 

< 

CD 

O 

a: 

Q. 


RANGE  (YD) 


Fig.  5 Comparison  of  lethality  per  aimed  shot  or  burst  for  the  M-l  Rifle  and 

the  Salvo  Automatic. 


exceed  the  M-l  rifle  by  about  a factor  of  three,  if  the  basic 
assumptions  used  in  the  estimates  can  be  accepted  as  rea- 
sonably valid.  Obviously,  at  ranges  less  than  100  yd, the 
dispersion  of  the  rounds  in  the  salvo  pattern  becomes  greatly 
diminished  as  range  is  decreased.  Consequently,  the  lethal 
effects  will  not  differ  greatly  from  the  single -round  rifle 
especially  when  zero  range  is  approached.  This  variation 
in  pattern  size  with  range  points  up  the  difficulty  of  attempt- 
ing to  assess  comparative  lethal  effects  at  the  shorter  ranges 
and  also  reveals  the  weakness  of  the  estimates  at  the  greater 
distances. 


IMATION  * 


Quite  apart  from  any  consideration  of  or  comment  upon, 
the  protocols  and  conventions  according  to  which  the  rules  of 
land  warfare  have  been  codified,  it  is  proper  to  estimate  in 
a purely  physical  way  the  results  of  the  use  of  toxic  missiles 
in  such  weapons. 

Consequently,  Fig.  5,  the  two  weapons  have  been  com- 
pared for  a use  of  toxic  missiles.*  It  is  interesting  to  note 
that,  by  the  addition  of  toxic  missiles  to  the  M-l  rifle,  the 
lethal  effects  thus  produced  are  about  equivalent  to  the 
theoretical  upper  limit  on  physical  effects  given  for  the  dis- 
persion weapon.  On  the  other  hand,  the  employment  of  toxic 
missiles  in  the  dispersion  weapon  offers,  in  toto,  still  greater 
gains;  such  effects  would  constitute  an  order  of  lethality  not 
achieved  by  any  missile  projecting  ground  weapon  yet  devised. 

Can  Lethality  Be  Increased? 

The  lethal  indices  of  present  weapons  cannot  be  improved 
materially  (if  at  all)  by  increasing  the  effective  "hitting  power" 
alone,  since  the  mortally  vulnerable  regions  of  the  body  set 
a limit  to  the  gain.  However,  by  combining  chemical  toxi- 
cants with  physical  missiles,  it  is  possible  to  make  the  entire 
body  vulnerable  by  utilizing  the  circulatory  system  as,  in 
effect,  a "missile  track"  which  produces  certain  lethal  effects. 
Rather  than  30  percent  fatalities  derived  from  bullet  hits,  this 
procedure  would  cause  the  body  to  become  mortally  vulnerable 
to  virtually  all  of  the  hits  received.  Quite  apart  from  the 
relative  increase  in  lethality  brought  about  by  the  design  of  a 
dispersion  weapon  as  shown  in  the  preceding  section,  the 
following  analysis  on  toxic  missiles  has  been  included  to  show 
the  nature  of  the  relative  gains  to  be  expected  in  the  dispersion 
weapon  if  toxicants  were  introduced  in  future  warfare.  The 
gains  to  be  described  are  purely  speculative  and  would  provide 
additional  gains  only  to  the  physical  lethality  of  the  dispersion 
weapon.  Although  not  a necessary  adjunct,  should  toxicants 
be  employed,  the  smaller  missiles  suggested  for  the  new  wea- 
pon would  be  more  efficient  vehicles  of  the  agent  than  the 
larger  .30  cal  bullets. 

Developmental  work  in  the  field  of  toxic  missiles  is  rea- 
sonably complete  and  shows  that  up  to  90  percent  of  hits  from 
agent-loaded  bullets  at  common  ranges  may  be  expected  to 

*As  indicated  later,  a lethal  probability  P = 0.9  was  assigned  to  each  toxic  loaded 
round.  The  curves  were  established  by  taking  the  product  of  the  probability  of  a hit 
and  the  probability  of  lethality  for  toxic  missiles.  (See  Table  A9  and  Fig.  A40.) 


f f 

l I ^ 


-160 


ORO-T-160 


29 


nplq  nr* 

incapacitate  in  a matter  of  minutes  and  bring  about  death 
regardless  of  the  region  of  the  body  struck.15  The  agent 
used  is  stable  (in  storage,  it  is  as  stable  as  any  other  part 
of  the  round);  it  can  be  manufactured  in  large  supply  at  low 
cost;  its  toxicity  is  about  as  high  as  any  substance  known. 

The  physiological  effects  produced  by  the  agent  are  similar 
to  the  G- agents:  death  is  rapid  and  the  course  of  the  effects 
is  violent.  The  progress  of  the  physiological  symptoms  is 
demoralizing  to  witness;  thus  real  psychological  effects  not 
normally  characteristic  of  weapons  design  are  added.* 

Since  it  has  been  found  that  small  missiles  (such  as  .22 
cal)  are  more  efficient  vehicles  for  such  toxic  agents  than  are 
the  larger  calibers/5  the  application  of  toxic  missiles  to  a 
small  caliber  hand  weapon  as  herein  proposed  is  particularly 
adaptable.  To  the  increase  in  hit  effectiveness  brought  about 
by  the  use  of  the  dispersion  weapon,  an  impressive  gain  in 
the  lethality  of  these  hits  might  be  added.  Thus  would  be 
achieved  a genuine  innovation  in  a weapons  system  which  has 
exhibited  through  history  a constancy  in  lethal  effects.** 

Data  from  the  last  two  World  Wars  show  that  for  ground  troops 
the  ratio  of  killed  to  wounded  (all  ground  weapons)  was,  for  both 
periods,  about  1:4.1.  About  20  percent,  then,  are  killed  in  action.1 
With  the  single  addition  of  toxic  bullets  for  small  arms  to  the 
whole  weapons  system,  the  ratio  of  KIA  to  WIA  in  these  past  two 
wars  would  have  been  raised  from  1:4.1  to  about  1:2.1,  or,  on 
the  average,  the  lethal  index  of  all  weapons  would  have  increased 
12  percent,  from  20  percent  to  32  percent.*** 

Although  these  figures  are  crude  estimates  of  the  gross 
or  over -all  gain  which  might  be  expected  by  the  employment 
of  toxic  missiles,  it  is  probable  that  the  gain  would  be  a 


Apart  from  flaming  weapons,  ordnance  development  has  not  taken  advantage  of  possible 
designs  to  produce  fear  in  the  enemy  as  well  as  physical  damage.  Toxic  missiles  do 
offer  the  possibility  of  combining  the  elements  of  physical  and  psychological  trauma  for 
maximum  effects.  [See  also  ORO-B-3,  Appendix  H,  (SECRET)] 

Against  toxic  missiles,  certain  defense  measures  could  be  adopted.  A suitable  antidote 
could  be  carried  by  each  man  in  the  form  of  an  ampule  and  injection  could  be  performed 
through  the  clothing  using  the  same  methods  as  planned  for  defense  of  G-agent 
poisoning.  Also,  if  small  caliber  missiles  were  used  and  the  bullets  were  designed  to 
encourage  rapid  disintegration  in  the  wound  track,  light  (plastic)  armor  might  be  used. 

In  both  of  these  areas  of  defense,  the  Soviet  may  be  weaker  than  the  US  in  the  initial 
phases  of  toxic  missile  employment  but  it  is  certain  that,  like  all  other  technical 
advantages  in  warfare,  a process  of  neutralization  will  occur  whereby  neither  side  has  a 
material  advantage  because  of  the  equalizing  effects  of  the  defense  measures  which 
both  sides  eventually  adopt.  Furthermore,  speedy  retaliation  in  kind  should  not  be 
difficult  for  either  side. 

Enemy  reactions  must  be  anticipated. 


30 


™>^  - I 


ORO-T-160 


* 


SEO 


NATION 


strategic  one  rather  than  tactical*  In  an  ORO  analysis  of 
battle  casualties  as  to  their  period  of  non-effectiveness,16 
data  indicate  that  ideal  toxic  missiles  would  do  little  further 
to  reduce  enemy  strength  during  any  battle  situation  but  may 
exert  considerable  influence  over  an  extended  campaign. 

Finally,  it  must  be  remembered  that  only  by  improving  the 
hit  capability  of  the  weapon,  as  herein  proposed  in  the  dis- 
persion weapon,  would  one  expect  maximum  gains  in  the 
tactical  situation  if  toxic  missiles  were  introduced. 

THE  DISPERSION  WEAPON 
Basis  of  Issue  (T/OkE) 

It  is  to  be  emphatically  stated  that  the  new  type  hand  arm, 
as  proposed  in  this  study,  should  not  entirely  replace  the  longer - 
range  rifle  in  the  unit  organization.  In  most  tactical  situations 
there  is  a definite  requirement  for  sniper  (highly  specialized) 
fire.  It  is  also  important  to  maintain  a degree  of  versatility 
responsive  to  the  dynamic  tactical  situation.  Consequently,  it 
is  believed  that  the  precision-aimed,  long-range  rifle  must  be 
retained  for  that  limited  but  existing  employment  which  its 
design  characteristics  actually  fit.  Limited  knowledge  of  sniper 
fire  indicates  that  at  squad  level  it  is  not  employed  frequently 
in  the  fire  fight  but  has  an  important  role  in  the  defense  or  in  the 
less  fluid  conditions  (maneuvering  for  build-up,  and  so  forth) 
preceding  a hot  action*  As  far  as  can  be  determined  by  ques- 
tioning combatants,  the  ranges  of  sniper  fire  are  mostly  within 
the  tactical  damage  range  of  the  small  caliber,  high  velocity 
missiles  (i,  e.  , up  to  800  yd).  This  suggests  the  possibility  of 
using  weapons  of  the  same  caliber  as  the  general  purpose  hand 
arm,  but  designed  for  precision,  long-range  use.  However, 
the  whole  question  of  sniper  fire  in  battle  is  yet  to  be  analyzed 
from  an  operations  point  of  view;  until  this  is  done  little  can  be 
said  concerning  weapons  requirements  for  specialists  in  this  role* 


About  20  percent  of  the  total  hits  of  these  past  wars  have  been  bullet  hits.  Of  those  hil 
roughly  30  percent  are  KIA.  (On  limited  knowledge  of  enemy  Japanese  rifles  of  WW  XT.) 
Thus,  toxic  bullets  would  result  in  90  percent  KIA  among  those  hit  and  increase  the 
lethality  of  the  bullet  by  a factor  of  3*.  Thus  the  total  killed  by  bullets  would  increase 
from,  20  X 0.3  — 6 percent  to  20  X 0.9  = 18  percent.  The  total  killed  (all  weapons) 
would  then  increase  from  20  percent  to  32  percent  of  those  hit,  (Note:  The  figure,  6 
percent,  for  fatal  bullet  hits  may  be  low  for  small  arms  fire;  Tribby’s  analysis  of  1,000 
KIA  in  the  ETO  attributed  about  11  percent  of  those  killed  to  small  arms  fire.) 


ORO-T-160 


31 


SECUR 


* IP*  3 

\ & 


\ ? ^ ^ ?t,7m 

The  question  of<  a general  purpose  hand  arm  is  not  one  of 


supplanting  a long-range  precision  arm,  but  rather  of  replacing 
a certain  number  with  a different  weapon,  each  type  having  its 
own  proper  and  effective  tactical  application. 

It  is  believed  that  a practical  and  useful  beginning  can  be 
made  in  deciding  upon  the  optimum  ratio  of  short-range  hand 
arms  to  long-range  precision  rifles  by  noting  the  figures  for 
ranges  of  engagement  which  have  been  presented  earlier.  On 
the  average,  it  has  been  found  that  70  percent  of  the  ranges  over 
which  a man-size  target  is  visible  to  a defending  rifleman  lie 
within  300  yd.  Since  the  short-range  weapon  will  be  designed 
according  to  specifications  for  maximum  effect  up  to  300  yd, 
it  may  be  suggested  that  7 in  every  10  infantry  hand  weapons 
should  have  the  characteristics  desirable  for  short-range  use. 
Although  this  target- visibility  criterion,  employed  to  set  an 
upper  limit  to  the  range  of  engagement,  ignores  certain  vari- 
ables within  the  small  infantry  unit  which  bear  on  control  and 
communications  as  well  as  many  of  the  problems  of  musketry 
and  maneuver,  it  may  be  received  as  a tentative  and  preliminary 
basis  for  issue. 

Another  approach  to  the  determination  of  an  optimum  ratio 
for  hand  weapons  is  to  consider  the  aptitudes  of  enlisted  men 
normally  received  from  the  manpower  pool.  From  experience 
at  Fort  Benning;*  the  development  of  no  more  than  two  expert 
riflemen  per  squad  may  be  expected  from  the  normal  recruit 
stream  without  special  training.  Unless  present  training  sched- 
ules and  methods  are  altered  to  permit  improvement  in  marks- 
manship skill,  this  tends  to  set  an  upper  limit  on  the  number  of 
highly  skilled  riflemen  that  it  is  feasible  to  assign  to  the  squad 
from  the  standpoint  of  natural  aptitudes  available  to  the  Army, 
and  of  the  training  effort. 

The  figure(two  experts  per  squad)  is  consistent,  however. 


This  does  not  mean  that  it  would  not  be  desirable  to  have  much 
higher  performance  in  marksmanship  among  all  the  men  in  the 
squad;  the  suggested  assignments  for  experts  merely  empha- 
size the  operational  need  for  at  least  two  experts  per  squad  if 
training  is  unavailing  in  raising  present  standards  of  performance. 

It  was  not  possible  to  obtain  data  from  the  AGO,  "G-3,  or  OCAFF  on  the  number  of 
enlisted  men  who  could  be  expected  on  the  average  to  pass  as  experts.  In  private 
communication  with  Fort  Benning,  the  Infantry  School  has  indicated  that  about  10 
percent  of  the  men  receiving  marksmanship  training  could  be  expected  to  pass  as 
experts  by  known  distance  range  firing  standards. 


with  that  already  given  as  the  apparent  actual  requirement. 


32 


ORO-T-160 


To  arrive  with  assurance  at  an  optimum  ratio,  much  more 
knowledge  of  small  unit  operations  in  combat  would  be  required 
than  is  now  known  in  ORO  or  elsewhere.  Determinations  at  a 
"tactical  laboratory,  " such  as  ORO  is  eager  to  see  established 
at  Fort  Benning,  could  contribute  much  to  the  solutions. 

Training 

The  increases  in  effectiveness  which  have  been  proposed  in 
this  analysis  all  follow  from  innovations  in  design  of  the  weapon 
for  the  purpose  of  overcoming  deficiencies  ip  skill  or  training 
and  for  adapting  the  weapon  to  the  nature  of  its  actual  opera- 
tional employment.  Since  there  ia  no  reason  to  suppose  that 
the  new  weapon  would  be  char  act  eric  ally  unlike  the  present 
rifle  in  its  method  of  operation,  no  increased  demands  for  train- 
ing time  or  facilities  are  visualized.  In  fact,  the  short  range 
of  the  weapon  offers  a chance  for  considerable  reduction  in 
weight  and  for  less  precision  in  working  parts.  Consequently, 
development  of  a lighter  weapon,  with  low  recoil,  should  facil- 
itate training  in  its  use. 

Also,  it  is  felt  that  men  would  react  favorably  to  a weapon 
which  increased  their  own  marksmanship  performance  since 
it  would  add  to  their  confidence  in  being  able  to  hit  the  enemy 
at  ranges  where  M-l  rifle  fire  is  comparatively  ineffective. 

It  does  not  seem  reasonable  to  assume  that  a man's  confidence 
in  his  weapon  would  be  affected  adversely  by  a design  which 
increased  his  chances  of  hitting  the  enemy  and  therefore  in- 
creased the  probability  of  his  own  survival. 

In  connection  with  present  marksmanship  training,  the  results 
given  in  the  Appendix  suggest  strongly  that  considerable  improve- 
ments are  needed  if  skills  are  to  approximate  the  precision  capa- 
bilities of  the  M-l  rifle.  An  examination  of  the  current  basic 
training  program  shows  that  76  hours  are  allowed  for  marksman- 
ship training  with  the  rifle,  of  which  only  48  hours  are  involved 
in  "wet"  exercises,  that  is,  actual  range  firing  of  the  weapon.17 

In  the  48  hours  of  training,  each  man  fires  at  least  400  rounds, 
which  indicates  roughly  the  total  amount  of  time  spent  in  the 
actual  employment  of  the  rifle.  Any  question  of  the  adequacy  of 
this  training  program  could  only  be  settled  by  field  tests  designed 
to  determine  the  best  methods  and  the  time  required  to  produce 
optimum  results  among  men  in  their  marksmanship  skills.  As 
shown  in  the  Appendix,  it  is  not  likely  that  training  alone  could 
be  effective  in  materially  raising  the  standards  of  all  men  to 
exceed  the  level  of  expert  performance  indicated  by  the  Belvoir 


ORO-T-160 


33 


tests.  Significant  gains  in  man -weapon  effectiveness  are  to  be 
obtained  only  by  combining  improvements  in  weapon  design  with 
good  training.  By  the  adoption  of  design  principles  in  a hand 
weapon,  as  proposed  in  this  study,  an  opportunity  is  offered  to 
realize  gains  of  considerable  magnitude. 

Design  Feasibility 

No  insoluble  problems  appear  to  be  involved  in  the  engineering 
of  a weapon  possessing  the  recommended  characteristics.  To 
accomplish  ideal  dispersion  in  an  automatic  hand  arm , as  ideal- 
ized in  the  Appendix,  many  design  difficulties  will  stand  in  the 
way  of  preserving  desirable  military  characteristics  such  as 
lightweight,  durability,  reliability,  automatic  loading,  and 
other  factors.  A salvo-type  automatic  which  projected  volleys 
of  rounds  to  form  the  desired  pattern  at  the  range  giving  maximum 
hit  effectiveness  probably  would  represent  the  best  type  of  design 
for  deriving  the  greatest  gains.  This  would  entail  designs  which 
include  the  multi -barrel  principle,  high  cyclic  rate  single-barrel 
types  with  a design  feature  for  allowing  the  barrel  to  nutate  at 
the  muzzle  on  recoil  for  controlled  dispersion,  frangible  missiles, 
aer ©dynamically  controlled  missiles,  compensators,  deflectors, 
and  the  like,  all  of  which  present  a variety  of  engineering  diffi- 
culties to  be  overcome  before  the  weapon  would  function  satis- 
factorily, The  point  of  chief  concern,  however,  is  to  strive  for 
the  attainment  of  the  pattern  dispersion  principle  so  that  the 
greatest  possible  gains  can  be  derived,  and  in  the  striving,  let 
the  engineering  difficulties  argue  for  themselves. 

In  studying  the  design  problems,  it  was  apparent  that  the 
smaller  caliber  weapon,  with  its  bullets  of  smaller  mass,  would 
have  considerably  less  recoil  than  present  automatics,  and  that 
the  reduced  dispersion  of  a burst,  along  with  the  employment  of 
a muzzle  compensator,  should  have  significant  effects  in  reducing 
muzzle  11  walk -off.  " As  stated  previously,  it  may  well  be  that  a 
light  automatic  of  small  caliber  (in  the  region  of  .20  cal)  would 
produce  dispersions  of  rounds  in  short  bursts  which  are  not 
incongruous  with  the  pattern  dispersions  specified  in  the  Appendix. 
At  least  the  tendency  would  be  a significant  reduction  in  dis- 
persion as  compared  to  present  automatics  with  their  high  recoil 
effects.  Such  reduction  may  be  sufficient  to  regard  the  dis- 
persion as  approaching  the  optimum  requirements. 

Considering  all  factors,  this  approach  to  the  problem  appears 
to  be  straightforward,  practical,  and  relatively  simple,  and  it 
offers  promise  of  fulfilling  the  desirable  optimum  dispersions 


£ : 


34 


ORO-T-160 


for  maximum  hit  effectiveness.  Tests  on  prototype  models  of 
new  weapons  of  small  caliber  should  be  made  to  determine  the 
practicality  of  this  approach  to  the  problem. 

A THEORY  FOR  DETERMINING 

RELATIVE  EFFECTIVENESS  OF  DIRECT  FIRE  WEAPONS 

The  analysis  would  not  be  complete  if  advantage  were  not 
taken  of  possible  valuable  theoretical  applications  which  may 
be  made  using  the  two  major  parameters  given  in  the  analysis 
of  the  man-rifle  system.  These  parameters  relate  to  the  prob- 
ability of  seeing  a man  target  on  the  battlefield  and  the  probability 
of  hitting  the  target  with  aimed  fire. 

To  test  an  hypothesis,  according  to  which  effectiveness  might  be 
evaluated,  use  was  made  of  battlefield  visibility  data  for  the  area 
of  Korea  where  ranges  were  known  for  a small  sample  of  rifle 
bullet  hits  among  members  of  the  Turkish  Brigade. 

Method  Used 

The  method  which  has  been  used  in  estimating  the  expected 
distribution  of  hits  as  a function  of  range  may  be  open  to  serious 
question  because  of  the  possible  weakness  of  the  assumptions 
made  about  actual  rifle  operations.  Although  the  need  was  recog- 
nized for  more  adequate  knowledge  of  the  factors  which  exert  a 
major  influence  on  aimed  rifle  fire,  it  was  felt  that  the  data  on 
visibility  and  hit  probability  might  be  useful  for  computing  the 
expected  distribution  of  hits  as  a function  of  range  for  different 
weapons.  As  shown  in  Table  1,  the  probability  product  of  the 
hit  data  and  of  the  visibility  data  for  each  range  interval  yields 
predictions  on  the  relative  distribution  of  hits,  if  one  assumes 
expenditure  proportional  to  targets  seen  and  targets  seen  pro- 
portional to  the  map  measurements  on  visibility. 

In  Table  1,  the  data  given  for  Ps  are  the  fraction  of  all 
cases  where  a man  can  be  seen  continuously  in  the  50-yd  inter- 
val. Employment  of  the  data  sets  up  a model  which  visualizes 
the  enemy  approaching  a defender  who  fires  on  the  enemy  when 
he  first  appears.  The  results  of  the  repetition  of  many  cases 
of  this  simple  dual  situation  should  permit  prediction  of  the 
type  of  distribution  of  hits  as  a function  of  range,  for  aimed  rifle 
fire  over  the  Korean  terrain.  While  it  is  possible  to  calculate 
the  number  of  hits  to  be  expected  as  a function  of  range  using 
column  4 of  th  er  of  hits  cannot  be 


ORO-T-160 


35 


:ORMATlON 


8 $ 


f > 

isV-Mi* 


I ^ 

r -rS-f'i  | 

, ......  *.viUuOL.ww  . , 

compared  with  the  observed  number  because  the  sample  of 
combat  data  did  not  provide  information  on  the  total  number  of 
men  involved  or  the  expenditure  of  rifle  ammunition.  For  this 
reason,  the  percentage  distribution  of  expected  hits  was  com- 
pared to  the  observed  distribution. 


TABLE  1 

COMPUTED  DISTRIBUTION  OF  HITS  AS  FUNCTION  OF  RANGE  R 


Range 
Interval,  yd 

Psa 

Phb 

Ps  x Ph 

Ps  x Ph, 
Normalized 

Accumulated 
“Expected 
Fraction 
of  Hits” 

0-49 

0.360 

1.00 

0.360 

0.457 

1.000 

50-99 

0.254 

0.93 

0.234 

0.297 

0.543 

100-149 

0.162 

0.76 

0.123 

0.156 

0.246 

150-199 

0.070 

0.54 

0.037 

0.047 

0.090 

200-249 

0.047 

0.38 

0.018 

0.023 

0.043 

250-299 

0.028 

0.28 

0.008 

0.010 

0.020 

300-349 

0.024 

0.22 

0.005 

0.006 

0.010 

350-399 

0.016 

0.17 

0.003 

0.004 

0.004 

Totals 

0.788 

1.000 

^Probability  of  seeing  target  within  each  interval. 
Probability  of  hit- 


In  Fig.  6,  the  distribution  for  the  calculated  fraction  of  hits 
corresponds  roughly  with  the  distribution  of  actual  hits  in  com- 
bat in  Korea. 

As  a matter  of  interest,  the  M-l  rifle  and  the  five-round 
salvo  type  weapon  were  compared  in  this  way  for  the  two  extreme 
types  of  terrain,  Class  A and  Class  C.  The  expected  distribution 
for  hits  from  both  weapons  at  ranges  greater  than  R for  the 
Korean  terrain  and  for  the  Normandy  terrain  is  given  in  Fig.  7. 
Since  these  distributions  do  not  show  the  relative  effectiveness 
of  the  two  weapons,  the  same  model  was  used  to  provide  an 
indication  of  the  merits  of  the  salvo  weapon  over  the  rifle  as 
terrain  influences  effectiveness. 

In  this  instance,  as  shown  in  Table  2,  the  hits  were  calculated 
on  the  basis  of  100  shots  fired  for  each  weapon  at  man  targets 
distributed  over  terrain  in  accordance  with  the  distribution  given 
for  Ps. 


36 


ORO-T-160 


5ECURI 


'ION 


PROBABILITY  OR  FRACTION 


r 


0 100  200  300  400  500 


R- RANGE  (YD) 

Fig.  6 — Rifle  marksmanship,  battlefield  visibility,  and  hit  probability  in 
combat.  A:  Ph,  probability  of  hitting  man-target  as  function  of  range; 
B,  observed  fraction  of  hits  occur ing  at  ranges  greater  than  R;  C,  proba- 
bility of  seeing  target  at  ranges  greater  than  R(l-Ps);  D,  computed  frac- 
tion of  hits  expected  to  occur  at  ranges  greater  than  R(Ps  x Ph,  where 
Ps  is  converted  to  frequency  of  visible  areas  occuring  in  each  50  yd 
interval,  and  where  Ph  is  averaged  in  each  interval  by  assuming  the 
mean  P value). 

* Assumes  expenditure  proportional  to  targets  seen  and  targets  seen  proportional 
to  Ps. 


ORO-T-160 


m 


INFORM? 


SECURITY 


HIT  PROBABILITY 


sulumi  i utmr  mmmmm 

A 


t yrt,  r*  J fy  f*  - 1 

j>  f1 


Fig.  7 — Theoretical  distribution  of  hits  as  function  of  range  for  M-l  Rifle  and  a Salvo- 
Type  Hand  Weapon  for  Class  "A”  and  *‘C”  Terrains. 


TABLE  2 

RELATIVE  EFFECTS  OF  M-l  SINGLE-ROUND  FIRE  AND  SALVO  FIRE 
AS  FUNCTION  OF  RANGE  FOR  TERRAIN  TYPES  A AND  C 


Range 
Interval*  yd 

Psa 

Phb 

Expected  Hits 

Ps  x Ph, 
Normalized 

Class  A 

Class  C 

M-l 

Salvo 

M-l 

Glass  A 

Salvo 
Class  A 

M-l 

Class  C 

Salvo 
Class  C 

0-49 

0.360 

0.05 

1.00 

1.00 

37 

37 

9 

9 

50-99 

0,254 

0.10 

0.93 

0.99 

24 

26. 

16 

17 

100-149 

0.162 

0.09 

0.76 

0.96 

12 

16 

12 

15 

150-199 

0.070 

0.09 

0.54 

0.89 

4 

6 

8 

14 

200-249 

0.047 

0.09 

0.38 

0.81 

2 

4 

6 

12 

250-299 

0.028 

0.06 

0.28 

0.71 

1 

2 

3 

9 

300-349 

0.024 

0.06 

0.22 

0.60 

1 

1 

2 

6 

350-399 

0.016 

0.04 

0.17 

0,49 

0 

1 

_1 

3 

Totals 

0.961 

0.58 

81 

93 

57 

85 

^Probability  of  seeing  target  within  each  interval 
■'probability  of  hit. 


38 


assiti 

mm  mm 


ORO-T-160 


100 


100 


80  — N 


\ 

\ 


\ 

\ 

\ 


CLASS  C TERRAIN 


(Normandy) 


0 


100 


200 


300 


400 


0 


100 


200 


300 


400 


RANGE  (YD) 


Fig.  8 — Relative  effectiveness  of  M-l  Rifle  and  Salvo  Automatic  for  Class  "A"  and 

"C”  Terrains. 


It  will  be  noted  in  Fig.  8 that  the  comparative  effectiveness 
of  the  salvo  weapon  is  much  greater  for  open  terrain  types  like 
Class  C than  for  terrain  types  of  Class  A because  of  the  greater 
hit  effectiveness  of  the  salvo  weapon  at  the  longer  ranges.  Such 
information,  although  only  relative,  suggests  that  the  dispersion 
type  hand  weapon  would  offer  material  advantages  over  the  M-l 
rifle  in  areas  of  combat  such  as  western  Europe.  On  the  other 
hand,  the  advantages  of  the  new  weapon  in  areas  like  Korea  are 
not  as  great  and  the  comparison  made  in  Fig.  8 supports  the 
contention  that  a hand  weapon  designed  for  semiautomatic  use 
in  the  short  ranges  and  for  full  automatic  use  in  the  longer 
ranges  with  controlled  dispersion  would  offer  a good  solution 
for  the  common  hand  arm. 

If  theory,  as  herein  presented,  can  be  confirmed  by  more 
extensive  knowledge  of  expenditure  and  ranges  of  hits  incurred 
in  combat  by  the  rifle  and  other  direct  fire  weapons  to  include 
machine  guns,  recoilless  rifles,  antitank  weapons,  and  the 
like,  the  method  would  constitute  a promising  basis  for  eval- 
uating a balanced  weapons  system,  and  T/O&E  for  units  might 
be  established  on  a quantitative  basis. 


ORO-T-160 


39 


f,  ? r*-  - 


CONCLUSIONS 


1.  The  ranges  at  which  the  rifle  is  used  most  frequently  in 
battle  and  the  ranges  within  which  the  greater  fraction  of  man 
targets  can  be  seen  on  the  battlefield  do  not  exceed  300  yd. 

2.  Within  these  important  battle  ranges,  the  marksmanship 
of  even  expert  riflemen  is  satisfactory  in  meeting  actual  battle 
requirements  only  up  to  100  yd;  beyond  100  yd,  marksmanship 
declines  sharply,  reaching  a low  order  at  300  yd. 

3.  To  improve  hit  effectiveness  at  the  ranges  not  covered 
satisfactorily  in  this  sense  by  men  using  the  M-l  (100  to  300 
yd),  the  adoption  of  a pattern-dispersion  principle  in  the  hand 
weapon  could  partly  compensate  for  human  aiming  errors  and 
thereby  significantly  increase  the  hits  at  ranges  up  to  300  yd. 

4.  Current  models  of  fully  automatic  hand  weapons  afford 
neither  these  desirable  characteristics  nor  adequate  alternatives. 
Such  weapons  are  valueless  from  the  standpoint  of  increasing 
the  number  of  targets  hit  when  aiming  on  separated  man- size 
targets. 

5.  Certain  of  the  costly  high  standards  of  accuracy  observed 
in  the  manufacture  of  current  rifles  and  ammunition  can  be  relaxed 
without  significant  losses  in  over-all  hit  effectiveness. 

6.  To  meet  the  actual  operational  requirements  of  a general 
purpose  infantry  hand  weapon  many  possibilities  are  open  for 
designs  which  will  give  desirable  dispersion  patterns  (and  accom- 
panying increases  in  hit  probability)  at  the  ranges  of  interest.  Of 
the. possible  salvo  or  volley  automatic  designs,  the  small  caliber, 
lightweight  weapon  with  controlled  dispersion  characteristics 
appears  to  be  a promising  approach.  (Low  recoil  of  a small  cal- 
iber weapon  facilitates  dispersion  control. ) 

7.  To  create  militarily  acceptable  wound  damage  at  common 
battle  ranges,  missiles  of  smaller  caliber  than  the  present  stand- 
ard .30  caliber  can  be  used  without  loss  in  wounding  effects  and 
with  substantial  logistical  and  over -all  military  gains. 

8.  A very  great  increase  in  hit  lethality  can  be  effected  by 
the  addition  of  toxic  agents  to  bullet  missiles. 


RECOMMENDATIONS 


1.  It  is  recommended  that  the  Ordnance  Corps  proceed  to 
determine  the  design  or  technological  feasibility  of  developing  a 


ORO-T-160 


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hand  weapon  which  has  the  characteristics  cited  in  this  analysis* 
namely: 


a.  Maximum  hit  effectiveness  against  man  targets  within 
300  yd  range.  (This  does  not  mean  that  the  weapon  will  be  ineffec- 
tive beyond  this  range. ) 

b.  Small  caliber  (less  than  .30). 

c.  Wounding  capability  up  to  300  yd  at  least  equivalent  to 
the  present  rifle. 

d.  Dispersion  of  rounds  from  salvos  or  bursts  controlled 
so  as  to  form  a pattern  such  that  aiming  errors  up  to  300  yd  will 
be  partly  compensated,  and  hit  effectiveness  thereby  increased 
for  these  ranges. 

2.  As  one  possible  alternative  to  the  current  "volume  of  fire" 
(fully  automatic)  approach  to  the  problem  of  increasing  the  effec- 
tive firepower  of  infantry  riflemen,  it  is  recommended— subject 
to  tentative  confirmation  of  design  feasibility— that  a rifle  incor- 
porating at  least  in  principle  the  military  characteristics  here 
proposed  be  manufactured  for  further  and  conclusive  test. 


ORO-T-160 


41 


lATION 


BIBLIOGRAPHY 


1.  Gardner,  John  H. ; Hitchman,  Norman  A.;  Best,  Robert  J, 

ORO-R-5:  ALCLAD  Final  Report,  Appendix  A. 

1 August  1951  (SECRET). 

2.  Johnson,  Ellis  A.;  Parker,  Edward  M.;  and  ORO  Staff. 

ORO-R-3:  MAID  Report,  Appendix  H. 

21  January  1950  (SECRET). 

3.  ORO-R-5,  Appendix  B (SECRET). 

4.  DeBakey,  M.  and  Beebe,  G.  Battle  Casualties.  Springfield, 

Illinois:  C.  Thomas  Co.,  1951  (UNCLASSIFIED). 

5.  Oughterson,  Col.  A.  W.  Wound  Ballistics  Report, 

Bougainville  Campaign,  1944  (RESTRICTED). 

6.  Office  of  the  Surgeon  General,  Wound  Ballistics  Survey, 

Korea  (15  November,  1950-5  May  1951)  (CONFIDENTIAL). 

7.  AORG  liaison  Letter,  December  1951  (SECRET). 

8.  Donovan,  Grace  N.  ORO-T- 18{FEC):  Use  of  Infantry  Weapons 

and  Equipment  in  Korea.  August  1952  (SECRET). 

9.  Kaye,  J.  D.  The  Use  of  Infantry  Weapons  in  Korea. 

ORS/Korea.  Report  No.  6,  12  March  1952  (SECRET). 

10.  Bayly  Pike,  D.  F.  and  Goepel,  Charles.  ORO-T-161:  The 

Effects  of  Terrain  on  Battlefield  Visibility  (SECRET). 

11.  Army  Field  Forces.  Report  of  Board  No.  3,  Project  2231, 

Vols.  I and  II.  Fort  Benning,  Georgia,  27  October  1950 
(SECRET). 

12.  National  Research  Council.  Missile  Casualty  Reports, 

Nos:  1 to  17. 

13.  Chemical  Corps  Medical  Laboratory,  Wound  Ballistics  of 

a .22  Caliber  Brass  Scale  Model  of  the  .30  Caliber  M-2 
Rifle  Ball,  Research  Report  No.  94,  December  1951 
(CONFIDENTIAL). 

14.  Hall,  D.  L.  An  Effectiveness  Study  of  the  Infantry  Rifle, 

BRLM  593,  March  1952  (CONFIDENTIAL). 

15.  Army  Chemical  Center.  Reports  on  Project  4-04-19-001 

(SECRET). 

16.  ORO  unpublished  Study. 

17.  FM-23-5,  US  Rifle  Cal  .30  M-l,  October  1951  (UNCLASSIFIED). 


42 


ORO-T-160 


sisuKT^5Erin!^®®^froN 


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i 


APPENDIX 

ANALYSIS  AND  APPLICATION  OF 
RESULTS  OF  RIFLE-RANGE  TESTS 


V 


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APPENDIX 


ANALYSIS  AND  APPLICATION 
OF  RESULTS  OF  RIFLE-RANGE  TESTS 

CONTENTS 


Page 

SUMMARY 

49 

INTRODUCTION 

49 

ANALYSIS 

50 

Objective  — Data  from  Tests  — Determination  of 
Means  (mpi)  and  Dispersion  (Standard  Deviation)  — 
Summary  of  Means  and  Standard  Deviation  — Disper- 
sion as  a Function  of  Range  — Systematic  Errors  in 
the  mpi  — Comparison  of  Observed  and  Theoretical 
Distributions  of  Deviations  from  mpi  — Remarks  on 
the  Homogeneity  of  Results  for  Individual  Riflemen  — 
Remarks  on  Deviations  of  mpi  from  Aiming  Point  — 
Comparison  of  Observed  and  Theoretical  Probabilities 
of  Hitting  Target  at  Various  Ranges  — Remarks  on 
Results  of  Firing  on  Targets  Appearing  Randomly  at 
Either  of  Two  Ranges. 

APPLICATION  91 

Theoretical  Probability  of  Hitting  Type  E Silhouette 
Target  With  a Salvo  Pattern  — Probabilities  for  1,2, 

3,4,  and  5 Hits  on  Man-Size  Target  With  Five-Shot 
Pattern  Salvo  — Comparison  of  Theoretical  Probabil- 
ities of  Hitting  “Average  Target"  with  Single -Shot 
and  Five-Shot  Pattern  Salvo  — Remarks  on  Significance 
of  Probabilities  of  Hitting  a Target  with  a Single-Shot 
and  with  Five-Shot,  Four -Shot  Pattern  Salvos  — Effect 


ORO-T-160  45 


IN 


Page 


^rvPI 


t > 


1 it*  on 


CONTENTS  (Continued) 


of  Weapon  Dispersion  on  Probability  of  Hitting 
Target. 


FIGURES 

A1-A32.  Shot  Patterns  on  Target  and  Screen,  Tests 
1 and  2. 


A33.  Example  illustrating  use  of  probability  paper 
to  determine  standard  deviations  and  means, 
whether  or  not  distribution  is  truncated 

A34.  Observed  standard  deviation,  Sr,  of  distance 
of  individual  shots  from  mpi  as  function  of 
target  range,  for  experts 

A35.  Observed  standard  deviation,  Sr,  of  distance 
of  individual  shots  from  mpi  as  function  of 
target  range,  for  marksmen 

A36.  Distance  of  mpi  from  top  of  target  as  function 
of  range 

A37.  Distance  of  mpi  from  vertical  line  through 
target  center  as  function  of  range;  Test  1 

A38.  Distance  of  mpi  from  vertical  line  through 
target  center  as  function  of  range;  Test  2 

A39.  Probability  of  expert  riflemen  hitting  Type  E 
silhouette  of  range 

A40.  Probability  of  marksmen  hitting  Type  E silhou- 
ette target  as  a function  of  range 

A41.  Probability  of  hitting  Type  E silhouette  target 

with  single  shot  compared  with  probability  of  at 
least  one  hit  with  a five -shot  pattern  salvo; 
curves  based  on  aiming  errors 


ORO- 


75 

76 
78 

80 

84 

85 

86 
88 
89 

92 

-160 


Imation 


FIGURES 

CONTENTS  (Continued) 

Pag 

A42. 

Probability  of  hitting  “average"  target.  A, 
with  single  shot  compared  with  probability 
of  at  least  one  hit  on  target  with  five-shot 
pattern  salvos. 

94 

A43. 

Probability  of  hitting  a circular  target  as 
function  of  range  for  several  weapon-ammu- 
nition errors 

97 

TABLES 

AI. 

Rifle  Range  Test  1 

98 

A2. 

Rifle  Range  Test  2 

99 

A3. 

Rifle  Range  Test  3 

100 

A4-5. 

Comparison  of  Observed  Number  of  Shots 
Inside  Zones  Bounded  by  Circles  of  Radii 
r i and  ^ in.,  with  Number  Expected  from 
Bivariate  Distribution  with  Radial  Standard 
Deviation  ar,  at  four  Ranges,  R,  in  yd. 

Test  1 (Ei  and  Es) 

101 

Test  1 (Mi  and  Ms) 

102 

A.6-7. 

Comparison  of  Observed  Number  of  Shots 
Inside  Zones  Bounded  by  Circles  of  Radii 
r^  and  r ^ in.,  with  Number  Expected  from 
Bivariate  Distribution  with  Radial  Standard 
Deviation  <7  r, at  four  Ranges,  R,  in  yd. 

Test  2 (Ei  and  Es) 

103 

Test  2 (Mi  and  Ms) 

104 

A8. 

Probabilities  for  Experts  Firing  Individually, 
of  Obtaining  Exactly  1,  2,  3,  4,  and  5 hits  on 
Type  E Silhouette  with  Five -Shot  Pattern 
Salvo  for  Indicated  Target  Ranges 

105 

A9. 

Probabilities  for  Marksmen  Firing  Indi- 
vidually, of  Obtaining  Exactly  1,  2,  3,  4,  and 
5 Hits  on  Type  E Silhouette  with  Five -Shot 
Pattern  Salvo  for  Indicated  Target  Ranges 

105 

ORO-T-160 


47 


TARGET  RANGE  DIAGRAM 


Therange  area  can  be  described  as  a common- looking  open-field  area  with  gentle  undulations 
in  the  ground  and  with  heavy  grass,  shrubs,  and  the  like  covering  the  surface  area  as  one 
would  see  in  relatively  open  country  in  many  parts  of  the  world. 


48 


ORO-T-160 


SiCURl 


lTION 


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BV1 

d E s 


i \J 


SUMMARY 


Results  of  expert  riflemen  and  marksmen  firing  at  man- size 
targets  at  different  ranges  were  analyzed  to  determine  aiming 
errors  as  function  of  range.  The  aiming  errors  in  mils  were 
found  to  be  independent  of  range.  Results  of  the  analysis  were 
used  to  compute  the  probability  of  hitting  targets  smaller  than 
the  man-size  target  and,  therefore,  more  realistically  repre- 
sentative of  the  average  area  presented  by  men  in  combat. 

Results  of  the  analysis  were  also  used  to  predict  the  probabilities 
of  hitting  targets  with  a hypothetical  weapon  firing  a five -shot 
pattern  and  a four -shot  pattern  salvo.  The  probability  of  obtain- 
ing at  least  one  hit  from  a single -salvo  firing  was  found  to  be 
decidedly  greater  than  the  probability  of  hitting  with  a single -shot 
weapon.  Probabilities  of  obtaining  multiple  hits  with  the  salvo- 
weapon  were  also  computed.  Finally,  the  effect  of  weapon  disper- 
sion on  the  probability  of  hitting  was  determined.  These  com- 
putations show  that  eliminating  the  weapon- ammunition  disper- 
sion would  not  materially  improve  the  rifleman's  hit  probability. 


INTRODUCTION 

In  the  BALANCE  study  of  the  Army  weapons  system,  examination 
of  the  basic  hand  arm  of  the  infantry,  the  rifle,  indicated  a need  to 
study  the  effectiveness  of  aimed  rifle  fire  on  man-size  targets  at 
ranges  of  combat  interest.  Heretofore,  marksmanship  has  been 
measured  by  scoring  hits  on  target  only,  and  sufficient  evidence  could 
not  be  obtained  on  the  nature  of  the  dispersion  (magnitude  of  errors) 
of  all  rounds  fired. 

To  provide  basic  parameters  for  the  whole  rifle  study,  a field  test 
was  conducted  at  Fort  Belvoir,  Ya.  , where  expert  riflemen  and 
marksmen  were  used  in  a series  of  experiments  designed  to  provide 
data  from  which  meaningful  conclusions  could  be  drawn.  Two  grades 
of  riflemen  (expert  and  marksman)  were  used  so  that  by  Army 
standards  the  upper  and  lower  limits  of  marksmanship  could  be 
studied.  By  having  the  men  fire  on  man- silhouette  targets  (type  E) 
at  battle  ranges  of  100-300  yd  on  a transition  type  range,  an  element 
of  combat  realism  was  provided.  In  order  to  record  and  measure 
the  dispersion  of  rounds,  target  screens  6 ft  high  and  12  ft  wide 
were  mounted  behind  the  silhouette  target  at  each  range.  The 
Appendix  Frontispiece  shows  the  design  of  the  range  used  and  the 
manner  in  which  targets  were  located. 


ORO-T-160 


49 


" Mini1 1 ^fON 


Dimensions  of  the  screens  and  test  procedures  were  products 
of  preliminary  trials  designed  to  determine  the  methodology  and 
physical  requirements  necessary  to  study  the  man-rifle  complex 
on  the  desired  basis.  The  target  butts  were  draped  with  OD  target 
cloth  so  that  rounds  below  the  target  and  screen  could  be  taken  into 
account  by  the  perforations  made  in.  the  cloth.  The  target  cloth  also 
was  useful  in  camouflaging  the  mounds  of  earth  at  each  target 
location. 

In  the  test  plan,  psychological  factors  which  might  have  arisen 
in  group  firing  were  eliminated  by  arranging  groups  of  experts  and 
marksmen  with  equal  representation  on  the  fire  line.  Also,  to 
remove  any  learning  effects  in  the  experiment,  the  order  of  fire  on 
targets  was  arranged  in  a manner  to  follow  a latin  square  type  of 
plan.  This  plan  allowed  each  man  to  complete  his  firing  serial  on 
four  ranges  by  ending  the  serial  on  the  target  with  which  he  had 
begun,  making  a total  of  five  target  shoots  on  four  ranges.  Learn- 
ing was  not  found  to  be  a significant  variable,  and  is  not  included 
in  the  analysis. 

Test  personnel  were  selected  according  to  marksmanship  scores 
from  13  training  companies  in  the  Engineer  Replacement  Training 
Center,  Fort  Belvoir,  Va.  Sixteen  riflemen  (eight  experts  and  eight 
marksmen)  were  used  on  each  of  the  two  tests  yriiich  were  conducted 
on  different  days.  Since  different  men  were  used  in  each  test,  a 
total  of  32  men  were  employed  in  the  whole  experiment.  The  follow- 
ing outline  shows  the  variety  of  conditions  studied  and  the  plan  of 
tests.  The  shots  on  target  and  screen  were  color-coded  in  each 
experiment  to  make  identification  possible.  All  firing  was  done  from 
the  prone  position  using  M-l  rifles  and  battle  sights. 

ANALYSIS 

Objective 

The  objective  of  the  analysis  was  to  determine  accuracy 
of  aimed  rifle  fire,  and  its  dependence  on  target  range,  for 
marksmen  and  experts  firing  the  M-l  rifle  under  the  conditions 
previously  described.  The  accuracy  thus  obtained  was  required 
as  a basis  for  predicting  with  reasonable  reliability,  the 
results  which  might  be  obtained  with  a hypothetical  weapon  of 
comparable  accuracy  which  could  fire  several  bullets  in  a pre- 
determined pattern. 

Data  from  Tests 

The  locations  of  bullet  holes,  derived  from  the  tests  are 


50 


ORO-T-160 


SECMfff  4HHf 


PLAN  OF  RIFLE  MARKSMANSHIP  TESTS 
Fort  Belvoir,  Va.,  27  Oct  and  10  Nov  1951 


Plan  of  Testa  1 and  2 


Purpose 

Subject 

Order  of  Fire 

Conditions 

To  evaluate 

E 

A-B-C-D-A 

Targets  (silhouettes)  exposed  for  3 sec 

individual 

M 

C-D-A-B-C 

every  3 sec.  For  each  exposure,  each  man 

marksmanship 

E 

B-A-D-C-B 

fired  one  round;  8 rounds  fired  per  man  per 

M 

D-C-B-A-D 

target.  Firing  done  in  4-man  serials. 

E 

A-D-C-B-A 

Conditions  repeated. 

M 

B-C-D-A-B 

E 

D-A-B-C-D 

M 

C-B-A-D-C 

E 

A-B-C-D-A 

Conditions  repeated. 

M 

C-D-A-B-C 

E 

B-A-D-C-B 

M 

D-C-B-A-D 

E 

A-D-C-B-A 

Conditions  repeated. 

M 

B-C-D-A-B 

E 

D-A-B-C-D 

M 

C-B-A-D-C 

To  evaluate 

8 

B-A-D-C-B 

Target  exposed  for  3 sec  every  3 sec. 

group 

experts 

Group  fired  simultaneously  at  each  range, 

marksmanship 

single  round  firing  for  each  exposure,  4 
rounds  per  target  per  man. 

8 

B-A-D-C-B 

Same  conditions  as  for  experts. 

marksmen 

Test  No.  3 

To  study 

4 

C-A-C-C-A-A-C-A 

Targets  exposed  for  only  1 sec,  alternate 

effects  of 

marksmen 

snap  shooting  at  two  target  ranges, 

rapid  fire 

schedule  of  exposure  shown  was  unknown 

when  order  of 

to  the  men.  Experiment  was  done  for 

target 

group  or  simultaneous  firing  and  for 

appearance 
is  unknown 

individual  firing. 

4 

C-A-C-C-A-A-C-A 

Same  as  above  conditions. 

experts 

KEY 


E Expert 
M = Marksman 
A ■=  Tgt  at  110  yd 


3 = Tgt  at  205  yd 
C = Tgt  at  265  yd 
D = Tgt  at  310  yd 


ORO-T-160 


51 


INCHES 


— ■if-™  tE(gFT^iiaHtittai» 

[.  | „ ^ f „ 

I >. 

shown  in  Figs.  A1  to  A3Z,  on  which  are  also  indicated  the  num- 
ber of  shots  which  were  fired  and  the  number  of  these  which  hit 
the  screen.  In  most  of  the  tests,  some  of  the  rounds  did  not  hit 
the  screen.  Most,  if  not  all,  of  these  were  observed  to  have  hit 
the  ground  in  front  of  the  screen.  While  the  percentage  of  shots 
hitting  the  target,  as  tabulated  in  the  last  column  of  Table  A1  is, 
of  course,  a function  of  accuracy,  it  does  not  provide  complete 
information  on  the  nature  of  the  dispersion  of  the  shot -pattern. 


Fig.  Al— 110  yard  range  (Test  No.  1),  expert  riflemen  firing  individually,  96  rounds  fired 
(8  each  by  12  men),  96  rounds  on  target  cloth,  88  rounds  on  target 


> ft 


i v 


SECIIBIIiM(C(B£LttSS&»AT10N 


52 


ORO-T-160 


-160  ORO-T-160 


6 

z 


o 

O- 


ui 


Fig.  A2 — 205  yd  range  (Test  No.  1),  expert  riflemen  firing  individually,  80  rounds  fired  (8  each  by  10 

men),  69  rounds  on  target  cloth,  36  rounds  on  target 


Unctenr» 


Fig.  A3— 265  yard  range  (Test  No.  1),  expert  riflemen  firing  individually,  72  rounds  fired  (8 
each  by  9 men),  62  rounds  on  targer  cloth,  34  rounds  on  target 


Fig.  A4 — 310  yard  range  (Test  No.  1),  expert  riflemen 
firing  individually,  72  rounds  fired  (8  each  by  9 men), 
47  rounds  on  target  cloth,  28  rounds  on  target 


54 


ORO-T-160 


INI 


J 

*0  50 


ids  fired  (8 


Fig.  A5 — 110  yard  range  (Test  No.  1),  expert  riflemen  firing  simultaneously,  32  rounds  fired 
(4  each  by  8 meri),  24  rounds  on  target  cloth,  20  rounds  on  target 


-T-160 


« 

ORO-T-I60 


55 


seMh  SECIW  THformatRW 


securi 


INFORMATION 


|s8( 


’•j 


Fig.  A6— 205  yard  range  (Test  No.  1),  expert  riflemen  firing  simultaneously,  32 
rounds  fired  (4  each  by  8 men),  26  rounds  on  target  cloth,  12  rounds  on  target 


1 rt  f"4  * s 


inrijis 


j t,  vjt  t y 


Qlliu 


56 


ORO-T-160 


iTION 


51 


MCMt 


ION 


usty,  32 
target 


Fig.  A7 — 265  yard  range  (Test  No.  1),  expert  riflemen  firing 
simultaneously,  32  rounds  fired  (4  each  by  8 men),  21  rounds 
on  target  cloth,  11  rounds  on  target 


Fig.  A8 — 310  yard  range  (Test  No.  1),  expert 
riflemen  firing  simultaneously,  32  rounds 
fired  (4  each  by  8 men)^  19  rounds  on  target 
cloth,  9 rounds  on  target 


INCHES 


40 


pi  ,,  110  yard  range  (Test  No.  1),  marksmen  firing  individuolly,  56  round.  fir^  (8  ooch  by  7 n.on)  - 8 round. 

Fig.  A9— 1 in  y«d  '«9«  l • round,  on  turgor  dolk,  39  round,  on  turgor 


u 

I 


o 


30 


20 


10 


10 


20 


INCHES 


Fig.  A9 110  yard  rang©  (Test  No.  1),  marksmen  firing  individually,  56  rounds  fired  (8  each  by  7 men) -8  rounds 

fired  by  Bates  not  included-56  rounds  on  target  cloth,  39  rounds  on  target 


O 

V 

O 

H 


O' 

o 


Fig*  A10— 205  yard  range  (Test  No.  1),  marksmen  firing  individually,  72  rounds  fired  (8  each  by  9 men),  58  rounds 

on  target  cloth,  T9  rounds  on  target 


<ji 

\D 


SECURITY 


SECURITY 


INFORMATION 


piper 

luOoj 


iO 


* K 

iTiprf 

! I a %uil 


Fig.  All 265  yard  range  (Test  No.  1),  marksmen  firing  individually,  72  rounds 

fired  (8  each  by  9 men),  65  rounds  hit  target  cloth,  25  rounds  hit  target 


Fig.  A12 310  yard  range  (Test  No.  1),  marksmen  firing 

individually,  80  rounds  fired  (8  each  by  10  men) -Bates 
excluded,  61  rounds  on  target  cloth,  24  rounds  on  target 


i tvi  ft 

uIaSo!ll0( 


60 


ORO-T-160 


RATION 


ORO-T-160 


I 

H 

t 

I—* 

o 

© 


flu 


J L 


J L 


Fig.  A13 — 110  yard  range  (Test  No.  1),  marksmen  firing  simultaneously,  32  rounds  fired  (4  each  by  8 men),  30  rounds  hit  target  cloth, 

12  rounds  hit  target 


WMATION 


ORO-T-160 


r 


Fig*  A14 — 205  yard  range  (Test  No.  1),  marksmen  firing  simultaneously,  32  rounds  fired  (4  each  by  8 meni 

19  rounds  on  target  cloth,  4 rounds  on  target 


mm 


w 


i /r*  f 

! . Nl 


Fig.  A15— 265  yard  range  (Test  No.  1),  marksmen  firing  simultaneously,  32  rounds  fired  (4  each  by 
8 men),  32  rounds  hit  target  cloth,  6 rounds  hit  target 


Fig.  A16 — 310  yard  range  (Test  No.  1),  marksmen  firing  simultaneously, 
32  rounds  fired  (4  each  by  8 men),  25  rounds  hit  target  cloth,  4 rounds 
hit  target 


ORO-T-160 


63 


Fig*  AI7 — 110  yard  range  (Test  No*  2),  expert  rifletnen  firing  individually,  96  shots  fired 
(8  each  by  12  men),  91  rounds  hit  target  cloth,  81  rounds  hit  target 


64 


pH  1 


ORO-T-160 


IATION 


Fig.  A18 — 205  yard  range  (Test  No.  2),  experts  firing  individually,  64  rounds  fired 
(8  each  by  8 men),  45  rounds  hit  target  cloth,  22  rounds  hit  target 


ORO-T-160 


65 


SECI 


INCHES  INCHES 


INFO'Ri 


Fig.  A19 — 265  yard  range  (Test  No.  2),  expert  riflemen  firing 
individually,  64  rounds  fired  (8  each  by  8 men),  56  rounds  on 
target  doth,  30  rounds  on  target 


Fig.  A20 — 310  yard  range  (Test  No.  2),  expert  riflemen  firing 
individually,  80  rounds  fired  (8  eoch  by  10  men),  77  rounds  hit 
target  doth,  35  rounds  hit  target 


66 


ORO-T-160 


ION 


iMATION 


* 


Fig.  A21 — 110  yard  range(Test  No.  2),  experts  firing  simultaneously,  32  rounds  fired  (4  each 
by  8 men),  28  rounds  hit  target  cloth,  28  rounds  hit  target 


n r*  I o o c*  ifi  £j  i 
I ii/lQwOli  IbU 


ORO-T-160 


67 


ORO-T-160 


CD 


\ 


Fig.  A22 — 205  yard  range  (Test  No.  2),  experts  firing  simultaneously,  64  rounds  fired  (4  each  by  16  men), 

58  rounds  hit  target  cloth,  19  rounds  hit  target 


Fig.  A23 — 265  yard  range  (Test  No.  2),  expert  riflemen  firing 
simultaneously,  32  rounds  fired  (4  each  by  8 men),  28  rounds 
on  target  cloth,  13  rounds  on  target 


Fig.  A24 — 310  yard  range  (Test  No.  2),  expert  riflemen  firing 
simultaneously,  32  rounds  fired  (4  each  by  8 men),  25  rounds 
hit  target  cloth,  8 rounds  hit  target 


ORO-T-160 


69 


INCHES 


m 


TION 


Fig.  A25 — 110  yard  range  (Test  No.  2),  marksmen  firing  individually,  64  shots  fired  (8  each 
by  8 men),  64  rounds  hit  target  cloth,  34  rounds  hit  target 


70 


GRO-T-160 


ATION 


09t-l-o*o 


1 


1 


1 


1 


Fig*  A26 — 205  yard  range  (Test  No.  2 ),  marksmen  firing  at  target  individual ly,  72  rounds  fired  (8 
each  by  9men)/  59  rounds  hit  target  cloth,  12  rounds  hit  target 


INFORMATION 


10 


0 


30 


20 


10 


0 


10 


20 


30 


40 


50 


60 


70 


INCHES 

Fig,  A27 — 265  yard  range  (Test  No.  2),  marksmen  firing  individually,  96  rounds  fired 
(8  each  by  12  men),  88  rounds  on  target  cloth,  19  rounds  on  target 


30  20  10  0 10  20  30  40  50  60  70 

INCHES 

Fig,  A28 — 310  yard  range  (Test  No.  2),  marksmen  firing 
individually,  80  rounds  fired  (8  each  by  10  men),  61  rounds 
hit  target  cloth,  12  rounds  hit  target 


70 


60 


50 


K 40 


20 


10 


0 


72 


SEC 


poi* 


by  16  men)  - 1 man  fired  5 rounds -49  rounds  hit  targetcloth,  lOrounds  hit 


Fig.  A31 — 265  yard  range  (Test  No.  2),  marksmen  firing 
s imultaneous  I yf  32  rounds  fired  (4  each  by  8 men),  24 
rounds  hit  target  cloth,  8 rounds  hit  target 


Fig.  A32 — 310  yard  range  (Test  No.  2),  marksmen  firing 
simultaneously,  32  rounds  fired  (4 each  by  8 men),  26  rounds 
hit  target  cloth,  2 rounds  hit  target 


ORO-T-160 


75 


x (IN.) 


and  Dispersion  (Standard  Deviation) 

As  already  indicated,  the  location  of  those  rounds  which  did 
not  hit  the  target  or  screen,  is,  of  course,  unknown.  How  then 
can  the  mean  (mpi)  and  dispersion  (standard  deviation)  be  deter- 
mined when  these  depend  on  the  actual  location  of  all  shots?  This 
problem  is  most  conveniently  solved  by  using  probability  paper  as 
illustrated  in  Fig.  A33. 


STANDARD  DEVIATION  (OR  MEANS)  LESS  THAN  THAT  INDICATED  BY  ORDINATE,  % 

Fig.  A33 — Example  illustrating  use  of  probability  paper  to  determine  standard  deviations 
and  means,  whether  or  not  distribution  is  truncated.  Data  are  from  Test  1,  experts  firing 
individually  at  205  yd. 

Suppose  x is  a variable  normally  distributed  about  mean  x, 
and  suppose  from  a sample  of  n x's  F,  is  determined,  where  Ft 
is  the  fraction  of  all  the  x's  in  the  sample  which  have  values  less 
than  xt,  and  F,  the  fraction  containing  all  values  of  x less  than 
Xj  (xt  >>  xt)and  so  on  to  Fn.  Then  for  a normal  distribution  of  the 
x's,  the  scale  of  F (abscissa  scale  of  Fig.  A33)  is  so  designed 
that  when  values  of  F are  plotted  against  the  corresponding  x , 
the  points  determine  a straight  line.  The  ordinate,  on  this  line, 
corresponding  to  abscissa  F =50  (i.  e.  , 50  percent)  determines 


60 


.01  o.i 


5 10  20  30  40  50  60  70  80  90  95  98  99  99.9  99.99 


76 


ORO-T-160 


y (IN.) 


r 


the  mean  of  the  sample.  If  this  mean  is  subtracted  from  the 
ordinate  corresponding  to  abscissa  F = 0.841,  the  difference  is 
the  estimated  standard  deviation  of  individual  values  about  the 
mean  of  the  sample. 

Thus,  the  upper  line  in  Fig.  A33  indicates  mean:  x = -0.5  inch 
and  standard  deviation:  Sx  = 13.5  in.  These  apply  to  the  x coordinates 
of  the  points  of  Fig.  A2.  Similarly  from  the  lower  line  in  Fig.  A33: 
y = 16.0  inches  (y  measured  from  bottom  of  screen  in  Fig.  A2)  and 
Sy=  15.0  inches.  The  percentages  (i.  e.  , abscissae)  for  the  points 
along  the  lower  line  of  Fig.  A33  were  computed  using  as  base  (i.  e. , 
100  percent)  the  total  number  of  shots  fired  (i.  e.  , 80  from  Fig.  A2), 
although  of  these  (11/80)  14  percent  were  off  the  screen  at  the 
bottom.  Thus,  even  though  the  distribution  of  y ' s is  truncated  at 
y - o (bottom  of  screen),  it  is  relatively  simple  to  estimate  the 
mean  and  the  standard  deviation  through  the  use  of  probability  paper 
which  incidently  facilities  the  calculation  even  for  the  nontrun- 
cated  case. 

On  the  other  hand,  if  the  distributions  of  x and  y are  statistically 
independent  (as  was  the  case  of  Fig.  A1  for  which  the  correlation 
between  x and  y did  not  significantly  differ  from  zero)  then,  refer- 
ring to  Fig.  A2,  the  mean  and  standard  deviation  of  x will  be 
independent  of  y.  Hence,  in  computing  the  percentages  (ordinates) 
for  the  upper  set  of  points  in  Fig.  A33,  it  was  essential  to  use  a 
base  (i.  e.  , 100  percent)  equal  to  the  number  of  shots  on  the  screen 
(i.  e.  , 69  from  Fig.  A2).  That  is  to  say,  the  distribution  of  the 
x’s  of  Fig.  A2  is  not  truncated,  as  was  that  of  the  y’s;  only  the 
sample  size  for  x is  diminished  as  a consequence  of  some  11 
shots  having  gone  off  the  screen. 

Summary  of  Means  and  Standard  Deviation 

Proceeding  as  described  in  the  preceding  paragraph,  the  means 
of  x and  y and  their  standard  deviations  were  determined  for  each  of 
the  test  results  shown  in  Figs.  A1  to  A32.  For  Tests  1 and  2,  the 
results  are  given  respectively  in  Tables  A1  and  A2.  Inspection 
of  Sx  and  Sy(i.  e.  , the  standard  deviations  of  x and  y)  in  Tables 
A1  and  A2  indicates  on  the  whole  no  very  great  difference  between 
Sx  and  Sy  . More  elaborate  tests  indicate  the  same  conclusion. 

For  example,  in  Test  1,  Table  1,  if  Sx  and  Sy  in  the  first  four 
rows  are  each  normalized  to  range  100  yd  (on  the  assumption  of 
constant  mil  error),  and  then  the  variance  of  x and  y are  sepa- 
rately pooled  (from  the  results  at  the  four  ranges),  the  resulting 
Sx  = 4.9  inches  and  Sy  = 5.8  inches,  a difference  of  only  18  per- 
cent. In  other  cases,  for  example,  in  Test  1 for  marksmen 


ORO-T-160 


77 


iILPJ 


t Jf  O Q ( T f p W 

firing  individually,  (M,,  Table  Al)  S exceeds  S . Hence,  on  the 
whole  no  serious  consequences  are  likely  to  arise  from  assuming 
°x  = ay  *or  the  results  (ax,  and  <ryare  standard  deviations  for 
the  whole  population). 


Dispersion  as  a Function  of  Range 

In  the  preceding  paragraph,  it  was  indicated  that  when  the 
standard  deviation  in  x (or  y)  at  each  of  the  four  ranges  was 
divided  by  the  range,  the  results  were  essentially  independent 
of  range.  It  was  also  indicated  that  x and  y were  independent 


Fig.  A34— -Observed  standard  deviation,  Sr,  of  distance  of  individual 
shots  from  mpi  as  function  of  target  range,  for  experts.  °,  Test  1;  +, 
Test  2;  I,  centered  at  from  combined  results  of  Tests  1 and  2. 
Total  vertical  extent  of  1 indicates  range  within  which  50  percent  of 
results  from  similar  samples  should  fall. 


1 * 1 

\ p n 

fr  <4  Li  .. 

L [ P. 

78 


ORO-T-160 


(i.  e. . correlation  zero)  and  that  their  standard  deviations  could 
be  assumed  equal.  This  suggests  the  standard  deviation  of 
r (r*  = x2  + yJ)  as  a convenient  measure  of  dispersion  since  it 
combines  Sx  and  Sy  (actually  Sr*  = SyJ  + Sxa). 

For  Tests  1 and  2 respectively,  values  of  Sr  are  listed  in 
column  7 of  Tables  A1  and  A2.  In  Figs.  A34  and  A35,  these 
values  of  Sr  are  plotted  as  a function  of  range  to  target.  It  is 
evident  in  Figs.  A34  and  A35  that  the  "observed"  values  of 
for  the  different  ranges  are,  within  the  indicated  statistical 
uncertainties,  reasonably  approximated  by  the  indicated  straight 
lines.  This  implies  that  the  dispersion  (standard  deviation)  in 
inches  at  the  target  increases  linearly  with  the  target  range, 
according  to  the  equations  indicated.  The  constants  show  that, 
in  accuracy,  the  riflemen  rank  in  the  following  order:  (1)  experts 
firing  individually,  (2)  experts  firing  simultaneously,  (3)  marks- 
men firing  individually,  and  (4)  marksmen  firing  simultaneously. 


Systematic  Errors  in  the  mpi 

Figure  A36  indicates  the  vertical  distance  of  the  mpi  from 
the  top  of  the  target,  at  the  four  ranges,  for  experts  and  marks- 
men in  Tests  1 and  2.  Even  if  all  men  aimed  at  the  center  of 
the  target,  vertical  systematic  deviations  of  the  mpi  from  the 
aiming  point  would  be  expected  as  a consequence  of  the  parabolic 
nature  of  the  bullet  trajectory.  How  the  vertical  coordinate  of 
the  mpi  varies  with  range  would  depend  on  the  range  for  which 
the  sights  are  set.  Figures  A37  and  A38  indicate  for  Tests  1 
and  2,  respectively,  the  x - coordinate  of  the  mpi  at  different 
ranges.  It  is  evident  that  in  Test  1 the  bias  is  quite  small'  and 
in  most  cases  probably  not  statistically  significant.  On  the 
contrary,  the  bias  in  Test  2 is  generally  larger  than  in  Test  1, 
particularly  for  marksmen,  and  is  in  many  cases  statistically 
significant.  Results  of  tests  for  the  significance  of  this  bias  are 
given  in  the  last  row  of  Tables  A4,  A5,  A6,  and  A7,  on  which 
further  comment  will  follow. 


Comparison  of  Observed  and 

Theoretical  Distributions  of  Deviations  from  mpi 

If  x and  y are  deviations  from  a mean,  and  are  independently 
and  normally  distributed  with  equal  standard  deviations,  ax  = a , 
then  it  is  convenient  to  consider  the  distribution  of  radial  y 
deviations,  r,  ^(r  = x + y ),  which  have  standard  deviation, 

°r  = (°x*  + CTy*)^-  14  can  be  shown  that,  of  all  the  radial  deviations 


ORO-T-160 


79 


INCHES  INCHES 


flwwSECItlT 


0 100  200  300  400 


RANGE  (YD) 


Fig.  A35 — Observed  standard  deviation,  $r,  of  distance  of  individual 
shots  from  mpi  as  function  of  target  range  for  marksmen.  For  meaning 
of  symbols  see  Fig.  A34. 


80 


ORCUT-160 


from  the  mean,  the  fraction  having  deviations  greater  than  or 
equal  to  kvr  is,  on  the  average,  given  by: 

W(k)  = e (1) 

or  looked  at  in  another  way  W(k)  is  the  probability  that  a shot 
falls  outside  the  circle  of  radius  r = kt7r  . The  following  table 
indicates  values  of  W(k)  for  a few  selected  values  of  k: 


k 

0.000 

0.536 

0.833 

1.179 

DO 

W (k) 

1.000 

0.750 

0.500 

0.750 

0.000 

In  particular,  the  circle  of  radius  0.833  ar,  with  W(k)  = 0.500, 
is  usually  called  the  circular  probable  error  (cpe).  Thus  circles 
of  radii,  o,  0.536  ar,  0.833  aT,  1.179  ar,  and  «,  with  centers  at 
the  mpi,  divide  the  plane  into  four  zones,  such  that  the  proba- 
bility of  a shot  hitting  within  any  one  of  the  zones  is  25  percent. 
These  circles  were  drawn  in  each  of  the  originals  of  Figs.  A1 
to  A32,  (but  they  are  not  reproduced  here),  and  the  radii  of  the 
circles  bounding  each  zone  are  listed  in  Tables  A4,  A5,  A6, 
and  A7.  These  tables  also  indicate  the  expected  and  observed 
numbers  of  shots  falling  in  each  zone. 

In  several  cases,  such  as  illustrated  in  Fig.  A4,  parts  of  some 
or  of  all  zones  are  off  the  screen.  For  these  cases  it  is  obviously 
impossible  to  indicate  how  those  shots  which  did  not  hit  the  screen 
were  distributed  among  the  zones.  In  such  instances  only  those 
shots  observed  to  hit  the  screen  can  be  properly  allocated  among 
the  partial  zones  which  are  on  the  screen.  The  expected  number 
of  hits  within  the  parts  of  zones  which  are  on  the  screen  is,  how- 
ever, computed  from  the  total  number  of  shots  fired  (72  in  the 
case  of  Fig.  A4).  This  was  done  using  circular  probability  paper 
to  facilitate  the  numerical  integration  to  determine  the  probability 
of  hits  falling  within  the  partial  zones.  Multiplying  these  proba- 
bilities by  the  total  number  of  shots  fired  gave  the  expected  num- 
ber of  hits  in  each  partial  zone. 

Corresponding  to  each  of  Figs.  A1  to  A32,  the  discrepancy 
between  the  observed  and  expected  number  of  hits  in  each  of  the 
four  zones  (or  partial  zones)  was  measured  by  y1.  P (*.*)  in 
Tables  A4,  A5,  A6,  and  A7  indicates  the  probability  of  obtaining, 
in  similar  samples,  as  bad  or  a worse  fit  between  observation 
and  expectation  than  that  indicated  in  the  Tables.  For  Test  1, 
the  values  of  P (ya)  in  Tables  A4  and  A5  are,  in  general,  large 
enough  so  that  the  fit  of  the  observed  distribution  to  the  theoret- 
ical one  is  acceptable.  Thus,  for  subsequent  calculations,  the 

ORO-T-160  81 


1AT10N 


more  convenient  theoretical  distribution  can  with  confidence  be 
used  in  place  of  the  observed  distribution.  The  discrepancy 
between  the  observed  and  theoretical  distributions  in  Test  2 are 
on  the  whole  greater  than  for  Test  1. 

Undoubtedly,  this  arises  either  from  a large  bias  in  the  mpi 
for  shots  fired  by  some  of  the  riflemen,  or  from  nonhomogeneity 
in  the  dispersion  for  all  the  riflemen.  However,  as  Figs.  A34 
and  A35  indicate,  the  radial  dispersions,  sr,  are  not  very  differ- 
ent in  the  two  tests  so  that  subsequent  conclusions  based  on  dis- 
persion indicated  by  the  straight  lines  (or  equations)  of  Figs.  A34 
and  A35,  will  not  be  much  in  error. 

Remarks  on  the  Homogeneity 
of  Results  for  Individual  Riflemen 

Attempts  were  made  to  identify  each  bullet  hole  according  to 
the  man  firing  in  the  case  of  those  tests  in  which  men  fired  indi- 
vidually. In  many  cases,  it  turned  out  that  holes  were  obviously 
improperly  marked.  Because  of  the  small  number  of  shots  fired 
by  each  man,  the  results  of  individuals  could  be  compared  reli- 
ably only  if  the  location  of  all  shots  fired  was  known.  Thus,  the 
comparison  of  individuals  is  limited  to  the  situation  of  Figs.  A1 
and  A9.  The  test  for  homogeneity  consisted,  in  the  case  of  Fig. 
Al,  in  counting  the  number  of  shots  each  individual  fired  inside 
and  the  number  outside  the  probable  error  circle,  and  testing 
this  against  the  expected  number  based  on  the  results  for  all 
riflemen.  The  following  table  indicates  the  results  for  Fig.  Al: 


Man  No. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

Total 

No.  inside9, 
p.e.  circle 

0 

4 

4 

5 

2 

5 

7 

7 

5 

6 

1 

2 

48 

No.  outside  a 
p.e.  circle 

8 

4 

4 

3 

6 

3 

1 

1 

3 

2 

7 

6 

48 

aThe  expected  number  throughout  is  4. 


Applying  the  ystest,  P = 0.003,  for  the  hypothesis  that  there 
is  no  difference  (in  the  long  run)  among  the  several  individuals, 
the  value  of  P indicates  a likelihood  of  some  difference  among 
the  individuals,  which  for  subsequent  purposes  is  not  serious, 
mainly  because  some  individuals  (Nos.  1 and  11)  appear  worse 
than  the  average,  while  others  (Nos.  7 and  8)  appear  better. 
This  somewhat  compensates,  so  that  the  distribution  of  all 
shots  does  not  deviate  seriously  from  the  expected  distribution 


82 


ORO-T-160 


N 


(see  P (y1)  Tables  A4,  A5,  A6,  and  A7).  Similar  tests  for  the 
results  in  Fig.  A 9 are  given  in  the  following  table: 


Man  No. 

1 

2 

3 

4 

5 

6 

7 

Total 

No.  insidea 
p.e.  circle 

1 

4 

5 

4 

7 

2 

4 

27 

No.  outside a 
p.e.  circle 

7 

4 

3 

4 

1 

6 

4 

29 

aThe  expected  number  throughout  is  4. 


Here  P (y2)  = 0.08,  indicating  no  statistically  significant  depar- 
ture from  homogeneity  of  results  for  the  seven  individuals. 


Remarks  on  Deviations  of  mpi  from  Aiming  Point 

In  connection  with  Fig.  A36,  it  is  reasonable  to  expect  some 
systematic  vertical  deviations  in  mpi  with  range;  because  of 
this,  tests  of  the  vertical  deviation  of  the  mpi  from  an  aiming 
point  were  not  made.  However,  deviations  of  the  mpi  to  the 
right  or  left  (x  coordinate)  from  the  vertical  line  through  the 
center  of  the  target  were  tested  to  determine  whether  they  were 
large  enough  to  be  statistically  significant.  The  results  are 
shown  in  Tables  A4,  A5,  A6,  and  A7  in  which  P (x)  indicates 
the  probability  of  obtaining  (in  further  samples  under  similar 
circumstances)  deviations  of  the  mpi  as  great  or  greater  than 
those  actually  observed.  It  is  evident  in  Tables  A4  and  A5  that, 
in  most  cases,  the  deviations  are  not  statistically  significant. 

For  Test  2 as  shown  in  Tables  A6  and  A7  several  small  values 
of  P were  obtained.  This  indicates  that  many  of  the  deviations 
are  statistically  significant,  particularly  since  Table  A2  and 
Fig.  A37  show  that  all  the  mpi,  in  Test  2,  deviated  to  the 
right  (x,  positive).  It  should  be  mentioned,  however,  that  if 
the  mpi  for  some  of  the  individual  riflemen  deviate  significantly 
from  the  mpi  averaged  for  all,  then  the  deviations  of  single 
shots  from  the  latter  mpi  are  not  statistically  independent. 

Taking  account  of  this  would  increase  the  values  of  P (x)  in  the 
Tables.  In  any  case,  the  deviations  of  the  mpi  (x  in  Tables  A4 
and  A5)  in  Test  1 were  not,  in  general,  significant  so  that 
subsequent  calculations  will  apply  reasonably  well  to  conditions 
of  Test  1. 

ORO-T-160  83 


10 


-X- 

100 


J- 

300 


400 




200 

RANGE  (YD) 


(§)  Experts  0 Marksmen 


Fig*  A3 6 — Distance  of  mpi  from  top  of  target  as  function  of  range; 
combined  individual  and  simultaneous  firings  of  experts  and  marksmen; 
Tests  1 and  2. 


84 


9C< 


ORO-T-160 


INCHES  , INCHES 


mm 


15 
10 
5 
0 

-5 
10 

0 100  200  300  400 

RANGE  (YD) 

O Experts  firing  individually  A Marksmen  firing  individually 

X Experts  firing  simultaneously  O Marksmen  firing  simultaneously 


15 


10 


5 


0 


”5 


-10 

0 100  200  300  400 

RANGE  (YD) 

Fig*  A37 — Distance  of  mpi  from  vertical  line  through  target  center  as 
function  of  range;  marksmen  and  experts  firing  individually  and 
simultaneous ly,  Test  1* 


ORO-T-160 


85 


INCHES  INCHES 


*^%*ECimnr 


O Experts  firing  individually 
X Experts  firing  simultaneously 


A Marksmen  firing  individually 
□ Marksmen  firing  simultaneously 


Fig.  A38 — Distance  of  mpi  from  vertical  line  through  target  center  as 
function  of  range;  marksmen  and  experts  firing  individually  and 
simultaneously.  Test  2. 


86  » C ORO-T-160 

L’  !■  ’ 

^'■yuamnnSratH-"  mPMMtioN 


siLuimii  5TIIIEI 11,1  lUiuiuMMi 


Comparison  of  Observed  and  Theoretical 
Probabilities  of  Hitting  Target  at  Various  Ranges 

Figures  A39  and  A40  compare  the  observed  and  theoretical 
probabilities  of  hitting  the  target  at  different  ranges  under  the 
several  conditions  involved  in  Tests  1 and  2.  The  observed 
probabilities  are,  of  course,  just  the  percentage  hits  on  the 
target,  from  Fig.  A1  to  A32.  The  theoretical  probabilities, 
shown  by  the  curves  of  Figs.  A3 9 and  A40  were  computed  on 
the  basis  of  the  following  model:  (a)  The  target  was  assumed 
to  have  the  shape  and  dimensions  shown  in  the  accompanying 
sketch: 


The  location  of  the  assumed  mpi  for  all  ranges  is  shown; 
it  is  on  the  vertical  center  line  through  the  target,  (b)  The 
standard  deviation  of  radial  deviations,  for  any  particular 
range,  was  assumed  to  be  that  given  by  the  lines  (or  equations) 
in  Figs.  A34  and  A35. 

Tests  show  that  the  deviations  of  some  of  the  "observed 
points"  from  the  curves,  in  Figs.  A39  and  A40,  are  statisti- 
cally significant.  These  deviations  are  generally  below  the 
curve.  In  Fig.  A40,  for  example,  all  the  crosses  in  the  upper 
figure  fall  below  the  curve.  Examination  of  Table  A2  indicates 
that  the  mpi  (the  x's  in  the  Table)  were  all  to  the  right  of  the 
vertical  center  line  through  the  target;  moreover,  the  small 
values  of  P (x)  in  Table  A7  indicate  that  these  deviations  of  the 


ORO-T-160 


87 


*™»  SMHEf 


tATSON 


PROBABILITY 


Fig.  A39 — Probability  of  expert  riflemen  hitting  Type  E silhouette  of  range.  Ei:  firing 
individually;  Es:  firing  simultaneously. 


88 


ORO-T-160 


isq 


SKRET WMfeRTION 


PROBABILITY 


Fig.  A40 — Probability  of  marksmen  hitting  Type  E silhouette  target  as  a function  of 
range.  Mi:  firing  individually;  Ms:  firing  simultaneously. 


ORO-T-160 


89 


mpi  from  the  center  line  were  statistically  significant.  Never- 
theless, the  curves  give  a fair  approximation  to  observed 
results,  at  least  for  Test  1.  In  fact,  the  differences  between 
the  theoretical  probabilities  of  hit  and  those  observed  in  Test  1 
are,  in  general,  comparable  with  the  differences  between  the 
observed  probabilities  in  Test  1 and  those  observed  in  Test  2. 

At  the  range  of  205  yd,  all  the  observed  points  fall  below  the 
curves.  In  Figs.  A34  and  A35  it  may  also  be  seen  that  the 
observed  standard  deviations  obtained  for  range  205  yd,  appear 
to  be  consistently  high.  Observers  at  the  firing  range  indicated 
that  the  target  appeared  to  be  as  far  away  as  that  at  265  yd. 

This  may  have  been  an  illusion  due  to  some  bushes  close  to 
the  line  of  sight.  If  sufficient  data  were  available  to  determine 
from  a large  number  of  samples  the  nature  of  the  distribution  of 
mpi,  this  could  be  used  in  the  determination  of  theoretical  proba- 
bilities. In  any  case,  the  theoretical  curves  and  the  hypotheses 
on  which  they  were  derived  provide  a convenient  and  sufficiently 
good  basis  on  which  to  compare  probabilities  of  hitting  targets 
with  a single-shot  weapon  and  a hypothetical  one  which  fires 
several  shots  simultaneously  in  a pattern. 


Remarks  on  Results  of  Firing  on  Targets 
Appearing  Randomly  at  Either  of  Two  Ranges 

Table  A3  indicates  the  results  obtained  when  the  target  (type 
E silhouettes)  appeared  randomly,  and  for  1 sec. , at  either  of 
two  ranges  (110  yd  or  265  yd)  as  described  in  the  introduction. 
Due  to  the  small  number  of  rounds  fired  and  especially  to  the 
very  small  number  of  hits  on  the  target,  inspection  of  Table  A3 
indicates  that  for  any  particular  range  the  differences  between 
the  percentage  hits  on  the  target  are  not  statistically  significant 
for  experts  firing  individually  (Ej)  compared  to  experts  firing 
simultaneously.  For  Test  3 the  same  conclusion  obtains  for 
marksmen.  Thus,  from  Table  A3  the  results  Ej  and  Ea  were 
combined  for  each  of  the  two  ranges;  results  for  and  Ms 
were  similarly  combined.  When  the  combined  results  for 
experts  in  Test3  at  range  110  yd  were  compared  with  the  results 
of  experts  firing  simultaneously  from  Tests  1 and  2,  at  110  yd, 
the  percentage  hits  on  the  target  were  definitely  less  in  Test  3, 
and  the  difference  was  found  to  be  statistically  significant.  Simi- 
larly, the  combined  results  for  experts  in  Test  3 at  265  yd 
indicated  a significantly  lower  percentage  hits  than  that  obtained 
from  the  combined  results,  in  Tests  1 and  2,  of  experts  firing 


90 


ORO-T-160 


simultaneously  at  range  265  yd.  That  is,  as  would  be  antici- 
pated, the  accuracy  of  expert  riflemen  for  the  same  range  was 
much  less  under  the  conditions  of  Test  3 than  under  the  conditions 
of  Tests  1 and  2.  For  the  marksmen,  the  results  from  Test  3 
were  not  statistically  different  from  those  of  Tests  1 and  2 
at  the  same  ranges. 


APPLICATION 

Theoretical  Probability  of  Hitting 

Type  E Silhouette  Target  With  a Salvo  Pattern 

In  the  same  way  that  the  results  of  the  present  analysis  were 
used  to  compute  the  curves  of  Figs.  A39  and  A40,  they  may  also 
be  used  to  obtain  the  variation,  with  range,  of  the  probability 
of  hitting  the  target  with  a salvo  pattern.  In  Fig.  A41,  the  curves 
M„(l)  and  Et  ( 1 ) are  respectively  the  curves  Ms  of  Fig.  A40,  and 
Ej  of  Fig.  A39.  The  curves  Ms(l)  and  Ej(l)  were  obtained  for  the 
target,  sketched  previously,  in  the  following  way:  The  right  half 
of  the  target  can  be  considered  made  up  of  two  rectangles:  one  5 
in.  x 38  in.  , and  the  other  5 in.  x 28  in.  ; with  A as  mean,  the 
independent  probabilities  of  x and  y falling  inside  each  of  the  rec- 
tangles are  readily  found  from  tables  of  the  probability  integral 
since  the  standard  deviations  of  x and  y are  known  for  any  range; 
for  each  rectangle  the  product  of  the  two  probabilities  gives,  of 
course,  the  probability  of  both  x and  y being  in  the  rectangle; 
summing  over  both  rectangles  and  multiplying  by  2 gives  the 
probability  of  hitting  the  target. 

In  Fig.  A41,  the  curves  Ej(2)  and  Mg (2)  were  computed  for 
the  five -shot  pattern  drawn  as  it  would  hit  a screen  at  300  yd 
range.  It  was  assumed  that  there  was  no  statistical  dispersion 
in  the  position  (at  the  target)  of  any  one  of  the  individual  missiles 
relative  to  the  others.  It  was  also  assumed  that  the  "spread"  of 
the  pattern  was  proportional  to  range.  The  dispersion  of  the 
center  missile  (the  others  in  the  pattern  remain  fixed  relative 
to  the  center  missile)  at  the  target  was  assumed  to  be  the  same 
as  that  used  in  computing  the  curves  E{  (1)  and  Ms(l),  i.  e.  , that 
derived  from  the  analysis  of  the  aiming  errors  obtained  in  the 
tests.  For  each  range  a "virtual  target"  was  drawn  such  that 
if  the  aimed  round  of  the  pattern  (i.  e. , the  central  one)  fell 
inside  the  boundary  of  the  virtual  target  then  at  least  one  missile 
hit  the  target.  Except  for  the  fact  that  the  "virtual  target"  was 
somewhat  more  complex  in  shape,  the  procedure  used  to  obtain 


ORO-T-160 


91 


PROBABILITY 


SECURITY 


INFORMATION* 


92 


Fig.  A41 — Probability  of  hitting  E type  silhouette  target  with  single 
shot  compared  with  probability  of  at  least  one  hit  with  a five-shot 
pattern  salvo;  curves  based  on  aiming  errors.  E*:  experts  firing  indi- 
vidually; Ms:  marksmen  firing  simultaneously;  (1)  with  single  shot; 
(2)  at  least  one  hit  with  five-shot  pattern  I;  (3)  at  least  one  hit  with 
five-shot  pattern  II. 


ORO-T-160 


secu ; 


iRMATJpN 


PROBABILITY 


SECURl 


Unclassified 

the  probability  of  obtaining  at  least  one  hit  was  the  same  as  that 
described  above  for  single  shots  (i.  e. , no  pattern). 

The  curves  Ej  (3)  and  Mg(3)  were  similarly  computed  for 
the  same  shape  of  salvo  pattern,  but  for  a pattern  with  half  the 
spread  (at  any  given  distance)  as  that  used  for  Et  (2)  and  Ma(2). 
From  Fig.  A41  it  is  evident  that,  of  the  two  shot  patterns,  the 
one  with  the  greater  spread  has  the  over -all  advantage  over 
ranges  up  to  300  yd.  Incidentally,  the  probability  of  at  least 
one  hit,  on  type  E silhouette,  indicated  by  curves  E.  (2)  and 
Ms(2),  Fig.  A41,  for  ranges  up  to  225  yd  applies  also  to  the 
four -shot  pattern  resulting  from  removal  of  the  center  shot  from 
pattern  I.  Curves  Ej  (3)  and  Ma(3)  apply  also  to  the  four -shot 
pattern  resulting  from  the  removal  of  the  central  bullet  of 
pattern  II. 


Probabilities  for  1.  2.  3,  4,  and  5 Hits 
on  Man-Size  Target  With  Five -Shot  Pattern  Salvo 

The  probabilities  of  1,  2,  3,  4,  and  5 bullets  hitting  a 
target  are  given  in  Tables  A8  and  A9  for  marksmen  and  for 
experts  individually  firing  a five -shot  pattern  salvo.  The 
target,  type  E silhouette,  is  that  sketched  previously.  The 
shot  pattern  used  in  the  calculations  is  pattern  I as  sketched 
in  Fig.  A41.  It  should  be  noted  that,  in  the  case  of  multiple 
hits,  the  individual  hits  are  not  located  at  random  relative  to 
each  other.  This  follows  from  the  assumptions  stated  previously 
to  the  effect  that  on  arrival  at  the  target  the  relative  positions  of 
all  missiles  in  the  pattern  are  fixed,  with  the  dimensions  of  the 
pattern  proportional  to  range. 

Comparison  of  Theoretical  Probabilities  of  Hitting 
"Average  Target"  with  Single -Shot  and  Five-Shot  Pattern  Salvo 
At  the  eye  of  a rifleman,  the  solid  angle  subtended  by  the 
average  human  target  in  combat  is  less  than  that  subtended  by 
the  type  E silhouette.1  For  the  approximation  to  the  average 
target  a rectangle  (for  convenience  in  calculation)  20  in.  x 12  in. 
was  chosen  and  designated  target  A (see  Fig.  A42).  The  proba- 
bility of  hitting  target  A as  a function  of  range  was  computed  giving 
the  results  shown  by  the  curves  in  Fig.  A42.  These  curves  indicate 
that  the  probability  of  at  least  one  hit  with  the  five -shot  pattern 
salvo  is  decidedly  greater,  for  the  same  range,  than  the  probability 
of  hitting  with  a single  shot.  If  the  central  bullet  is  removed  from 


lORO-R-5 


ORO-T-160 


93 


PROBABILITY 


SECURI^tKHW^FORMATION 


1 


RANGE  (YD) 


CO 

< 

CO 

O 

£L 


Fig*  A42 — Probability  of  hitting  “average"  target,  A,  (sketched  in 
box)  with  single  shot  compared  with  probability  of  at  least  one  hit  on 
target  with  five-shot  pattern  salvos.  E j : experts  firing  individually; 
M$:  marksmen  firing  simultaneously;  (4)  with  single  shot;  (5)  at  least 
one  hit  on  target  with  five- shot  pattern  I. 


94 


ORO-T-160 


SECI 


In 


the  five -shot  pattern  the  probability  of  at  least  one  hit  on  target  A 
is  unaffected  at  ranges  less  than  150  yd. 

Remarks  on  Significance  of  Probabilities  of  Hitting  a Target 
with  a Single-Shot  and  with  Five-Shot,  Four -Shot  Pattern  Salvos 
Although  the  probability  of  at  least  one  hit  on  the  target  is,  at 
the  same  range,  greater  for  one  five -shot  pattern  salvo  than  for 
a single  shot,  it  is  less  then  the  probability  of  at  least  one  hit  on 
the  target  for  five  separately  aimed  single  shots.  Consider,  for 
example, the  comparison  at  200  yd  range  for  the  upper  curves  in 
Fig.  A42.  For  the  five -shot  pattern,  curve  Ej(5)  indicates  at 
200  yd  a probability  of  about  0.74  for  at  least  one  hit.  For  one 
single  shot,  curve  Eg  (4)  indicates  about  0.32  for  the  hit  probability. 
The  probability  of  at  least  one  hit  in  five  single-shot  trials  is  then: 

(1  - 0.68*)  = 0.85  which  is  somewhat  greater  than  the  probability 
of  0.74  for  at  least  one  hit  for  the  five-shot  pattern. 

Consider  also  the  case  for  range  150  yd  for  target  A.  The  curve 
Eg  (4)  of  Fig.  A42  shows  for  range  150  yd  a probability  of  0.49  for 
hitting  target  A.  Curve  E.  (5)  indicates  0.90  for  the  probability  of 
at  least  one  hit  using  the  five-shot  pattern.  As  indicated  in  the 
preceding  section,  the  probability  of  at  least  one  hit  for  the  four- 
shot  pattern  (central  one  of  the  five-shot  pattern  removed)  is,  for 
ranges  less  than  150  yd,  the  same  as  for  the  five-shot  pattern. 

Thus,  the  probability  of  at  least  one  hit,  in  this  case,  from  five 
single  shots  is  (1  - 0.51s ) = 0.97  which  is  slightly  greater  than  that 
for  at  least  one  hit  from  a single  five -shot  pattern  salvo.  However, 
if  we  use  a four-shot  pattern  we  find  (1  - 0.5 14  ) = 0.93  for  the  proba- 
bility of  at  least  one  hit  from  four  single  shots  compared  to  0.90 
for  the  probability  of  at  least  one  hit  from  the  four -shot  pattern. 
Thus,  for  targets  which  may  remain  in  the  rifleman's  view  only 
long  enough  for  him  to  aim  once,  the  advantages  of  the  five -shot 
pattern  salvo  are  evident. 

Effect  of  Weapon  Dispersion  on  Probability  of  Hitting  Target 

In  order  to  determine  the  effect  of  weapon  dispersion  (the 
dispersion  at  the  target  when  the  rifle  is  rigidly  fixed)  on  the 
probability  of  hitting  the  target,  it  is  necessary  to  determine  the 
standard  deviation  due  only  to  aiming.  From  the  firing  test  data 
the  total  standard  deviation,  at  , at  the  target  was  found  to  be 
proportional  to  the  range,  that  is 

aT  ~ cr  in.  (l) 

with  r the  range  in  units  of  100  yd. 

• » i * Jjf 

ORO-T-160  95 


SEC  I 


»<B« 


Let  trw  represent  the  standard  deviation  due  to  weapon  dispersion 
(i.  e.  , standard  deviation  of  shot  distances  from  mpi).  Now  the 
standard  deviation  at  the  target,  due  only  to  weapon  dispersion, 
will  also  be  proportional  to  the  range  r,  then: 


Also  the  standard  deviation,  <7A,  due  to  aiming  errors  only  (i.e.,no 
weapon -ammunition  dispersion)  will  be  proportional  to  the  range,  thus: 


Since  deviations  from  the  mpi  due  to  aiming  errors  and  to  weapon- 
ammunition  errors  are  independent,  than  at  a particular  range: 


Tests  on  the  M-l  rifle  indicate  that  a=  2.3  in.;  that  is,  the 
standard  deviation  of  shot  distances  from  the  mpi,  for  a rigidly 
held  rifle,  is  2.3  in.  at  100  yd.  (i.e.,  r = 1),  including  dispersion 
due  to  ammunition.  This  determines  A in  Equation  5 when  c is 
known.  From  Table  A5  the  value  of  c is  9.0  in.  for  marksmen 
firing  individually.  For  this  case,  and  using  oc=  2.3  in.,  Equation 
5 determines  A = 76.  Thus  for  other  weapon  dispersions,  k x 2.3, 
the  variance^2  of  the  combined  errors  due  to  weapon- ammunition 
and  aiming  is  given  by: 


Consider  target  A which,  as  previously  described,  is  a rectangle 
20  in.  x 12  in.  The  probability  of  hitting  this  target  (mpi  at  center) 
is, to  a degree  of  approximation  sufficient  for  present  purposes,  the 
probability  of  hitting  a circular  target  with  the  same  area.  Thus, 
for  convenience  in  estimating  the  effect  of  weapon  dispersion  on 
probability  of  hitting,  consider  the  circular  target  with  radius  a 
such  that  it  s?  = 240  in.2  , (12  in.  x 20  in.)  from  which  a2  = 76.5 
(a  = 8.75  in.).  For  the  mpi  at  the  center  of  the  circle,  the  probability, 
Pm,  of  missing  the  target  (i.e.  , of  shots  falling  outside  the  circle 
of  radius  a)  is: 


for  marksmen  firing  individually.  The  three  lines  designated 


crw  = Otr  in. 


(2) 


= At  in. 


(3) 


o; 


T 


2 


aK  + < 


2 


(4) 


or  for  any  range  r: 


A2  r*  +0tk2r2 


(5) 


'r 


2 


= r2  (76  + 5k2) 


(6) 


p. 


m 


e 


-76.5/r*(76  + 5k2)  ^ 


in  Fig.  A43  are  the  curves  of  Equation  (7)  for  each  of  three  values 


96 


ORO-T-160 


5EO 


M&MfwaiftyioN 


3: 


y* 


o 

QC 

< 

O 

z 

I- 


LL 

O 


_J 

cfi 

< 

£0 

O 

Q£ 

CL 


Fig.  A43 — Probability  of  hitting  a circular  target  of  area  = 240  sq  in.  (radius  = 8.75  in.) 
as  a function  of  range  for  several  weapon-ammunition  errors.  Plotted  for  marksmen 
firing  individually,  Mj;  and  experts  firing  individually,  Ej.  k is  a selected  multiple  of 
the  standard  deviation  of  the  strike  from  the  mpi,  as  caused  by  weapon  and  ammunition 
alone.  Thus  k - 1 represents  actual  performance  with  issue  rifle  and  ammunition,  k =0 
shows  performance  with  perfect  weapons  and  ammunition,  and  k = 2 indicates 
performance  with  weapons  and  ammunitions  giving  double  the  actual  standard  deviation. 


of  k.  From  these  curves  (Mj)  it  will  be  seen  that  the  probability 
of  hitting  for  K = 0 (i.e.,  no  weapon -ammunition  dispersion)  is 
only  slightly  less  than  k = 1 (i.e.,  for  the  actual  dispersion  of 
the  M-l  rifle  and  ammunition).  Also,  the  curves  for  k = 2 
indicate  probabilities  of  hitting  which  are  still  not  significantly 
less  than  those  for  a dispersionless  rifle  and  ammunition  (k  = 0). 
The  four  lower  curves  (Ej)  in  Fig.  A43  apply  to  experts  firing 
individually,  for  which  the  equation  is: 

P = e "aVV  = e -76.5/r»(42.5+5k2) 
m ' * 

Equation  8 is  obtained  in  the  same  manner  as  Equation  7 starting 
with  the  value  of  6.9  in.  for  c,  obtained  from  Table  A4  for  experts 
firing  individually. 


ORO-T-160 


ORO-T-160 


00 


TABLE  A1 

RIFLE  RANGE  TEST  1 


Men 

Range, 

y* 

Std. 

Deviation,  in. 

No.  Men 

Rounds 

Total 

No*  Rounds 

% on 

yd 

/ in* 

in. 

X 

y 

r 

Firing 

per  man 

Rounds 

Target 

Screen 

Target 

Eia 

110 

- 0.9 

13*5 

4.1 

5.2 

6.4 

12 

8 

96 

88 

96 

0.917 

205 

- 0.5 

16.0 

13.5 

15.0 

20.2 

10 

8 

80 

36 

69 

0.450 

265 

~ 3.0 

19.5 

13*0 

13*0 

18.4 

9 

8 

72 

34 

62 

0.472 

310 

+ 6.0 

7.0 

12.6 

17.8 

21.8 

9 

8 

72 

28 

47 

0.389 

Esb 

110 

+ 1.2 

8.7 

4.1 

11.2 

11.9 

8 

4 

32 

20 

24 

0.625 

205 

- 2.8 

15.6 

11.0 

12.8 

16*9 

8 

4 

32 

12 

26 

0.375 

265 

- 5.9 

11.0 

8*4 

17.2 

19.1 

8 

4 

32 

11 

21 

0.344 

310 

- 8.2 

10.0 

15*0 

18.3 

23.7 

8 

4 

32 

9 

19 

0,281 

Mie 

110 

- 1.7 

16.4 

8.7 

6.4 

10.8 

7 

8 

56 

39 

56 

0*696 

205 

- 2*0 

15.2 

13*0 

14.5 

19.5 

9 

8 

72 

19 

58 

0.264 

265 

+ 4.8 

18.3 

17*2 

14.0 

22*2 

9 

8 

72 

25 

65 

0.347 

310 

- 1.0 

14.8 

24.0 

12.2 

26.9 

10 

8 

80 

24 

61 

0*300 

Msd 

110 

- 1.8 

14.2 

14.2 

9.0 

16.8 

8 

4 

32 

12 

30 

0.375 

205 

+ 10.5 

11.8 

23.0 

20.2 

30.6 

8 

4 

32 

4 

19 

0*125 

265 

- 2.5 

31.5 

25.1 

13,9 

28.7 

3 

4 

32 

6 

32 

0.188 

310 

+ 1.0 

17.2 

36.0 

15.8 

39.3 

8 

4 

32 

4 

25 

0.125 

- Expert  Riflemen  Individually  Firing  at  Target.  - Marksmen  Individually  Firing  at  Target. 

Eg  - Expert  Riflemen  Simultaneously  Firing  at  Target.  - Marksmen  Simultaneously  Firing  at  Target. 


ORO-T-160 


TABLE  A2 

RIFLE  RANGE  TEST  2 


Men 

Range, 

yd 

x, 

in. 

y * 

in. 

Std. 

Deviation,  in. 

No.  Men 
Firing 

Rounds 
per  man 

Total 

Rounds 

No.  Rounds 

% on 
Target 

X 

y 

r 

Target 

Screen 

E.a 

110 

+ 

0.6 

15.4 

5.2 

6.9 

8.6 

12 

8 

96 

81 

91 

0.844 

1 

205 

+ 

5.7 

18.0 

14.8 

14.5 

20.7 

8 

8 

64 

22 

45 

0.344 

265 

+ 

3.4 

14.1 

9.4 

13.1 

16.1 

8 

8 

64 

30 

56 

0.469 

310 

+ 

12.5 

23.5 

13.5 

13.1 

18.8 

10 

8 

80 

35 

77 

0.438 

Esb 

110 

+ 

0.8 

20.5 

2.8 

9.3 

9.7 

8 

4 

32 

28 

28 

0.875 

205 

+ 

3.9 

23.0 

17.1 

14.3 

22.3 

16 

4 

64 

19 

58 

0.297 

265 

+ 

1.7 

17.0 

10.1 

12.8 

16.3 

8 

4 

32 

13 

28 

0.406 

310 

+ 

2.5 

13.9 

21.5 

14.1 

25.7 

8 

4 

32 

8 

25 

0.250 

Mjc 

110 

+ 

5.8 

23.4 

6.8 

7.1 

9.8 

8 

8 

64 

34 

64 

0.531 

205 

+ 

14.1 

26.6 

23.1 

17.9 

29.2 

9 

8 

72 

12 

59 

0.167 

265 

+ 

15.2 

20.2 

19.5 

11.4 

22.6 

12 

8 

96 

19 

88 

0.198 

310 

+ 

19.1 

17.0 

24.1 

23.3 

33.5 

10 

S 

80 

12 

61 

0.150 

M d 

no 

+. 

2.2 

26.7 

10.5 

8.1 

13.3 

8 

4 

32 

18 

29 

0.562 

s 

205 

+ 

12.1 

24.5 

18.5 

18.0 

25.8 

16 

4 

65e 

10 

49 

0.154 

265 

+ 

9.2 

14.4 

12.7 

20.1 

23.8 

8 

4 

32 

8 

24 

0.250 

310 

+ 

10.8 

21.3 

17.2 

23.7 

29.3 

8 

4 

32 

2 

26 

0.062 

®E.  - Expert  Riflemen  Individually  Firing  at  Target,  - Marksmen  Simultaneously  Firing  at  Target. 

bE1g  - Expert  Riflemen  Simultaneously  Firing  at  Target.  eQne  Man  Fired  Five  Rounc*s. 

CM.  - Marksmen  Individually  Firing  at  Target. 


100  ORO-T-160 


TABLE  AS 


RIFLE  RANGE  TEST  3 

FIRING  AT  TARGETS  NO*  1 AND  NO.  3 ALTERNATELY  ON  RANDOM  SCHEDULE 


Men 

Range, 

yd 

x, 

in. 

y * 

in. 

Std. 

Deviation,  in. 

No.  Men 
Firing 

Rounds 
per  man 

Total 

Rounds 

Number  Rounds 

% on 
Target 

Not 

Expend. 

On 

Target 

On 

Screen 

X 

y 

r 

E.a 

110 

- 4.4 

16*8 

20.2 

21.4 

29.4 

4 

4 

15 

1 

4 

11 

0.267 

265 

0.0 

23.0 

20.0 

15.9 

25.6 

4 

4 

16 

0 

1 

13 

0.062 

Eab 

110 

+ 4.0 

7.9 

18.0 

11.3 

21.3 

4 

4 

11 

5 

2 

7 

0.182 

265 

+ 4*0 

* 8.0 

21.0 

24.8 

32.5 

4 

4 

16 

0 

0 

6 

0.000 

Mic 

110 

- 1.8 

16.7 

13.4 

8.7 

16.0 

4 

4 

14 

2 

7 

14 

0.500 

265 

- 1.4 

6.9 

41.1 

23.5 

47.3 

4 

4 

15 

1 

1 

8 

0.067 

Msd 

110 

- 10.8 

13.0 

11.6 

15.4 

19.3 

4 

4 

13 

3 

4 

10 

0,308 

265 

- 2.7 

- 7.0 

15.4 

19.5 

24.8 

4 

4 

16 

0 

3 

6 

0.188 

- Expert  Riflemen  Individually  Firing  at  Target. 

Eg  - Expert  Riflemen  Simultaneously  Firing  at  Target, 


- Marksmen  Individually  Firing  at  Target, 
aMg  - Marksmen  Simultaneously  Firing  at  Target. 


TABLE  A4 


.ON 


COMPARISON  OF  OBSERVED  NUMBER  OF  SHOTS  INSIDE  ZONES 
BOUNDED  BY  CIRCLES  OF  RADII  rt,  AND  ra,  IN.,  WITH 
NUMBER  EXPECTED  FROM  BIVARIATE  DISTRIBUTION  WITH  RADIAL 
STANDARD  DEVIATION  ax\  AT  FOUR  RANGES,  R,  IN  YD:  TEST  1 


(A)  Experts  Individually  ot  = 6.9  R/100  {at  in  in.) 

(<7  = a = 4.87  R/100,  in.) 
x y 


R(yd)  110 

205 

265 

310 

ffr  7.6 

14.1 

18.3 

21.4 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

r r 

1 2 

Obsd  Exptd 

r r 

1 2 

Obsd  Exptd 

r r 

1 2 

Obsd  Exptd 

r r 

t 2 

Obsd  Exptd 

0 4.1 

4.1  6.3 

6.3  9.0 

9.0  <» 

25  24 

28  24 

23  24 

20  24 

0 7.6 

7.6  11.7 
11.7  16.6 
16.6  •» 

15  20 

14  20 

18  20 

33  20 

0 9.8 

9.8  15.2 
15.2  21.6 

21.6  oc 

23  18 

19  18 

12  18 

18  18 

0 11.5 

11.5  17.8 
17.8  25.2 
05.2  B)b 

20d  16d 

12d  12d 

7*1  lld 

On  Screen 
Off  Screen 
Total 

P(x2) 

P(x) 

96 

0 

96  96 

0.75 
0.10 

69 

Ua 

80  80 
0.01 
0.66 

62 

10a 

72  72 

0.25 
0.05 

47  50 

25°  22° 

72  72 

0.5 
10~4 

(B)  Exp 

erts  Simultaneously  aT  = 7.8  R/100  (<rr  in  in.) 
{a  = a =*  5.51  R/100,  in.) 

x y 

R(yd)  110 

205 

265 

310 

aT  8.6 

16.0 

20.7 

24.2 

Zone 

No*  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

r r 

l .2 

Obsd  Exptd 

r r 

1 2 

Obsd  Exptd 

r r 

1 2 

Ob$d  Exptd 

r r 

1 2 

Obsd  Exptd 

0 4.6 
4.6  7.1 
7.1  10.1 
10.1 

9 8 

5 8 

4 8 

14  8 

0 8.6 

8.6  13.3 
13.3  18.9 
18.9  L~ 

8 8 

7 8 

5 8 

12  8 

0 11.1 

11.1  17.2 

17.2  24.4 
@4.4  B)b 

7 8 

5d  5d 

2d  5d 

0 13.0 

13.0  20.1 

20.1  28.5 
@8,5  B)b 

3d  6d 

4d  5d 

On  Screen  24 
Off  Screen  8a 
Total  32  32 

P(X2>  0.05 

P(x)  0.27 

26 

6a 

32  32 

0.75 
0.17 

21  24 

11°  7° 

32  32 

0.4 
0.02 

19  24 

13c  8C 

32  32 

0.25 
0.01 

aOff  screen  in  outermost  zone.  *|Off  screen;  zone  unknown. 

^Outside  but  on  screen.  “Within  zone  and  on  screen. 

p ( X2  ) probability  of  obtaining  as  bad  or  worse  fit  between  observed  and  expected  numbers. 
P ( X ) probability  of  obtaining  mpi  as  far  or  farther  from  vertical  center  line  of  target. 


ORO-T-160 


101 


TABLE  A5 

COMPARISON  OF  OBSERVED  NUMBER  OF  SHOTS  INSIDE  ZONES 
BOUNDED  BY  CIRCLES  OF  RADII  r„  AND  r2,  IN.,  WITH 
NUMBER  EXPECTED  FROM  BIVARIATE  DISTRIBUTION  WITH  RADIAL 
STANDARD  DEVIATION  af\  AT  FOUR  RANGES,  R,  IN  YD:  TEST  1 


(A)  Marksmen  Individually  ar  = 9.0  R/100  (a  in  in.) 

(a  = a = 6.36  R/100,  in.) 

x y 


R(yd)  110 

205 

265 

310 

aT  9.9 

18.4 

23.9 

27.9 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Obsd  Exptd 

*1  r2 

Obsd  Exptd 

rl  r2 

Obsd  Exptd 

ri  r2 

Obsd  Exptd 

0 5.3 

5.3  8.2 

8.2  11.7 
11.7  « 

18  14 

10  14 

11  14 

17  14 

0 9.9 

9.9  15.4 
15.4  21.8 
(21.8  B)b 

11  18 

10,  18h 

13d  15d 

24d  13d 

0 12.8 

12.8  19.9 

19.9  28.0 
(28.0  B)b 

«,  18h 

18d  18d 

20d  14d 

12d  12d 

0 15.0 

15.0  23.2 
23.2  32.9 
(32.9  B)b 

22  20 

14d  16d 

15d  16d 

10d  12d 

On  Screen  56 
Off  Screen  0 
Total  56  56 

P(X*)  0.25 

P(x)  0.07 

58  64 

14a  8a 

72  72 

10 
0.07 

65  62 

7a  10a 

72  72 

0.3 
0.02 

61  64 

19a  16a 

80  80 

0.9 
0.7 

(B)  Marksmen  Simultaneously  = 13.0  R/100  (ar  in  in.) 

{a  = a — 9.2  R/100,  in.) 

x y 


-R(yd)  110 

205 

265 

310 

or  14.3 

r 

26.6 

34.5 

40.3 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

ri  ra 

Obsd  Exptd 

ri  r2 

Obsd  Exptd 

Obsd  Exptd 

ri  *2 

Obsd  Exptd 

0 7.7 

7.7  11.9 
11.9  16.9 
(16.9  B)b 

5 8- 

7 8 

9d  8d 

9d  6d 

0 14.3 

14.3  22.2 
22.2  31.4 
(31.4  B)b 

4d  8d 

2d  6d 

8d  5d 

5d  4d 

0 18.4 

18.4  28.7 
28.7  40.6 
(40.6  B)b 

11  8 

13d  8d 

3d  5d 

5d  3d 

0 21.6 

21.6  33.6 

33.6  47.5 
(47.5  B)b 

lld  8d 

A ftd 

Id  Jd 

Sd  2d 

On  Screen  30  30 

Off  Screen  2a  2a 

Total  32 

P(X»)  0.5 

P(x)  0.3 

19  23 

13a  9a 

32  32 

0.1 

2 x 10 

32  24 

0a  Sa 

32  32 

0.01 
0.6 

25  20 

7a  12a 

32  32 

0.2 
0.8 

®Off  screen,  zone  unknown. 

^Outside  rx  but  on  screen. 
aWithin  zone  and  on  screen. 

P(X2)  probability  of  obtaining  as  bad  or  worse  fit  between  observed  and  expected  numbers. 
P ( x ) probability  of  obtaining  mpi  as  far  or  farther  from  vertical  center  line  of  target. 


102 


ORO-T-160 


f ; 


TABLE  A6 

COMPARISON  OF  OBSERVED  NUMBER  OF  SHOTS  INSIDE  ZONES 
BOUNDED  BY  CIRCLES  OF  RADII  r„  AND  r4,  IN.,  WITH 
NUMBER  EXPECTED  FROM  BIVARIATE  DISTRIBUTION  WITH  RADIAL 
STANDARD  DEVIATION  of  AT  FOUR  RANGES,  R,  IN  YD:  TEST  2 


(A)  Experts  Individually  oT  - 6.9  R/100  (erf  in  in.) 

{a  = o = 4.87  R/100,  in.) 
x y 


R(yd)  110 

205 

265 

310 

o,  7.6 

14.1 

18.3 

21.4 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Obsd  Exptd 

pi  r* 

Obsd  Exptd 

r i 

Obsd  Exptd 

ri  P2 

Obsd  Exptd 

0 4.1 

4.1  6.3 

6.3  9.0 

9.0  °° 

15  24 

23  24 

22  24 

36  24 

0 7.6 

7.6  11.7 
11.7  16.6 
16.6 

9 16 

8 16 

9 16 

38  16 

0 9.8 

9.8  15.2 
15.2  21.6 
21.6  B)c 

20  16 

14  j 16 

14“  13“ 

8d  lld 

0 11.5 

11.5  17.8 
17.8  25.2 
25.2  B)c 

21  20 

31  20 

On  Screen  9 1 
Off  Screen  5a 
Total  96  96 

P(x*)  0.02 

P(x)  0.25 

45 

19a 

64  64 

<0.001 
3x10"* 

56  56, 

8b  8b 
64  64 

0.71 
0.04 

77  76 

3b  4b 

80  80 

0,02 
2 x 10”9 

(B)  Experts  Simultaneously  &r  = 7.8  R/100  (at  in  in.) 

(ff  = = g,51  R/100,  in.) 

* y 


R(yd) 

110 

205 

265 

310 

°r 

8.6 

16.0 

20.7 

24.2 

Zone 

No.  in 

Zone 

Zone 

No.  in 

Zone 

Zone 

No.  in 

Zone 

Zone 

No.  in 

Zone 

Ti  T2 

Obsd 

Exptd 

ri  r2 

Obsd 

Exptd 

ri  r2 

Obsd 

Exptd 

P1  p2 

Obsd 

Exptd 

0 4.6 

6 

8 

0 8.6 

6 

16 

0 14.1 

10 

8 

0 13.0 

8, 

8, 

4.6  7.1 

8 

8 

8.6  13.3 

10 

16 

11.1  17.2 

9, 

8, 

13.0  20.1 

2d 

7d 

7.1  10.1 

11 

8 

13.3  18.9 

15 

16 

17.2  24.2 

sj 

20.1  28.5 

7? 

ej 

10.1  oo 

7 

8 

18.9  oq 

33 

16 

24.4  B)c 

ld 

6d 

28.5  B)c 

8d 

5d 

On  Screen 

28 

58 

29 

29, 

25 

26 

Off  Screen 

4a 

6a 

4b 

3b 

7b 

6b 

Total 

32 

32 

64 

64 

32 

32 

32 

32 

PCx1) 

0.63 

<0.001 

0.26 

0.23 

P(x) 

0.49 

0,01 

0.52 

0.42 

f'Off  screen  in  outermost  zone. 
DOff  screen,  zone  unknown. 

P(  x1 ) probability  of  obtaining 
P ( x ) probability  of  obtaining 


^Outside  rx  but  on  screen. 
aWithin  zone  and  on  screen. 

as  bad  or  worse  fit  between  observed  and  expected  numbers, 
mpi  as  far  or  farther  from  vertical  center  line  of  target. 


ORO-T-160 


103 


si 


DECLASSIFIED 


TABLE  A7 

I 

COMPARISON  OF  OBSERVED  NUMBER  OF  SHOTS  INSIDE  ZONES 
BOUNDED  BY  CIRCLES  OF  RADII  r„  AND  ra,  IN.,  WITH 
NUMBER  EXPECTED  FROM  BIVARIATE  DISTRIBUTION  WITH  RADIAL 
STANDARD  DEVIATION  at  AT  FOUR  RANGES,  R,  IN  YD:  TEST  2 


(A)  Marksmen  Individually  at  = 9.0  R/100  (at  in  in.) 

(<7  = a = 6.36  R/100,  in.) 

x y 


R(yd)  110 

205 

265 

310 

ar  9.9 

18.4 

23.9 

27.9 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

i1  r2 

Obsd  Exptd 

r2 

Obsd  Exptd 

ri  *2 

Obsd  Exptd 

ri  ra 

Obsd  Exptd 

0 5.3 

5.3  8.2 

8.2  11.7 
11.7  ~ 

13  16 

21  16 

16  16 

14  16 

0 9.9 

9.9  15.4 
15.4  21.8 
21.8  ~ 

9 18 

9 18 

12  18 

42  18 

0 12.8 

12.8  19.9 

19.9  28.1 

28,1  B)° 

32  24 

20  24h 

27“  20“ 

9d  17“ 

0 15.0 

15.0  23.2 
23.2  32.9 
32.9  B)c 

13,  20 

13d  18d 

17d  14d 

18d  13d 

On  Screen  64 

Off  Screen  0 

Total  64  64 

PCX1)  0-50  _ 

P(x)  <2  xl0“* 

59 

13a 

72  72 

<0.001 
<2xl0*9 

88  85 

8b  llb 

96  96 

0.04 

<2  xlO-9 

61h  65 

19b  15b 

80  80 
0.12 

<2x10“^ 

(B)  Marksmen  Simultaneously  oj.  = 13.0  R/100  (ffr  in  in.) 

(a  = cr  = 9.2  R/100,  in.) 
x y 


R(yd)  110 

205 

265 

310 

or  14.3 

26.6 

34.5 

40.3 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

Zone 

No.  in  Zone 

*2 

Obsd  Exptd 

*1  *2 

Obsd  Exptd 

*1  *2 

Obsd  Exptd 

r2 

Obsd  Exptd 

0 7.7 

7.7  11.9 

11.9  16.9 

16.9  .» 

13  8 

9 8 

3 8 

7 8 

0 14.3 

14.3  22.2 
22.2  31.4 

31.4  B)° 

16  16 

10 , 16d 

13d  15d 

10d  12d 

0 18.5 

18.5  28.7 
28.7  40.6 

40.6  B)c 

13  8 

8d  6d 

3d  5d 

0d  5d 

0 21.6 

21.6  33.6 

33.6  47.5 
47.5  B)c 

13  8 

8d  6d 

8H  5d 

2d  5d 

On  Screen  29 
Off  Screen  3a 
Total  32  32 

p(x2>  0.09 

P(x)  0.23 

49l  59 

16b  6b 
65  65 

<0.001 
<2  xlO”9 

24h  24 

8b  8b 
32  32 

0.05 
0.04 

26  24h 

6b  8b 
32  32 

0.15 
0.03 

^Off  screen  in  outermost  zone.  ^Outside  r1T  but  on  screen. 

bOff  screen,  zone  unknown.  Within  zone  and  on  screen. 

P ( ) probability  of  obtaining  as  bad  or  worse  fit  between  observed  and  expected  numbers. 

P ( x ) probability  of  obtaining  mpi  as  far  or  farther  from  vertical  center  line  of  target. 


104 


DECLASSIFIED 


ORO-T-160 


INFORMATION 


TABLE  A 8 


PROBABILITIES,  FOR  EXPERTS  FIRING  INDIVIDUALLY, 
OF  OBTAINING  EXACTLY  1,  2,  3,  4,  AND  5 HITS 
ON  TYPE  E SILHOUETTE  WITH  FIVE-SHOT  PATTERN 
SALVO  FOR  INDICATED  TARGET  RANGES 


Range,  yd 

Exact  No.  of  Hits 

At  least 
1 hit 

1 

2 

3 

4 

5 

100 

0.040 

0.002 

0.049 

0.420 

0.489 

1.000 

150 

0.174 

0.041 

0.269 

0.506 

0.000 

0.990 

200 

0.325 

0.145 

0.398 

0.091 

0.000 

0.959 

250 

0.423 

0.353 

0.125 

0.000 

0.000 

0.901 

300 

0.546 

0.280 

0.000 

0.000 

0.000 

0.826 

350 

0.524 

0.165 

0.000 

0.000 

0.000 

0.689 

400 

0.499 

0.087 

0.000 

0.000 

0.000 

0.586 

TABLE  A9 

PROBABILITIES,  FOR  MARKSMEN  FIRING  INDIVIDUALLY, 
OF  OBTAINING  EXACTLY  1,  2,  3,  4,  AND  5 HITS 
ON  TYPE  E SILHOUETTE  WITH  FIVE  -SHOT  PATTERN 
SALVO  FOR  INDICATED  TARGET  RANGES 


Range,  yd 

Exact  No.  of  Hits 

At  least 
1 hit 

1 

2 

3 

4 

5 

100 

0.111 

0.011 

0.093 

0.415 

0.360 

0.990 

150 

0.271 

0.066 

0.250 

0.350 

0.000 

0.937 

200 

0.388 

0.122 

0.284 

0.058 

0.000 

0.852 

250 

0.434 

0.240 

0.085 

0.000 

0.000 

0.759 

300 

0.482 

0.186 

0.000 

0.000 

0.000 

0.668 

350 

0.436 

0.108 

0.000 

0.000 

0.000 

0.544 

400 

0.398 

0.057 

0.000 

0,000 

0.000 

0.455 

; U < 


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6JblO  Connecticut  Avenue 
Chevy  Chase,  Maryland 


a aa'^gas 


18  November  1952 


SUBJECT:  Distribution  of  Project  BALANCE  Technical  Memorandum,  QR0-T-160, 

"Operational  Requirements  for  an  Infantry  Hand  Weapon." 


TO:  The  Deputy  Assistant  Chief  of  Staff,  G-3, 

for  Research,  Requirements  and  Special  Weapons 
Department  of  the  Army 
Room  3E37U,  The  Pentagon 
Washington  25,  D.  C. 


1.  References: 

a.  Memorandum,  Office  of  the  Assistant  Chief  of  Staff,  G-3, 
Operations,  f?.le  G-3  Oli.0  ORO,  dated  22  October  1952,  subject:  Department 
of  the  Army  Operations  Research  Office  Publication." 

b.  Letter,  Office  of  the  Assistant  Chief  of  Staff,  G-3,  RR&SW, 

dated  8 August  1952,  subject:  "Distribution  List  for  Project  BALANCE." 

2.  a.  Pursuant  to  paragraph  2,  a.  Inclosure  No.  1,  reference  a, 
advance  copies  of  0R0-T-160,  "Operational  Requirements  for  an  Infantry 
Hand  Weapon,"  by  Norman  Hitchman,  Scott  Forbush,  and  George  Blakemore, 

Jr.,  are  transmitted  herewith. 

b.  It  is  requested  that  authority  be  given  for  the  distribution 
of  this  document  according  to  the  basic  Operations  Research  Office  distri- 
bution list,  as  supplemented  by  the  Project  BALANCE  list  of  reference  b, 
and  to  include  all  the  optional  addressees  on  the  latter  list. 

3.  The  findings  and  suggestions  presented  in  this  technical  memo- 
randum reflect,  on  the  one  hand,  facts  already  experimentally  determined; 
and,  on  the  other,  certain  emergent  principles  relative  to  the  operational 
effectiveness  of  the  general  issue  rifle.  Many  of  these  principles  re- 
quire further  experimentation  in  order  conclusively  to  fix  details  of 
their  application.  Restatement,  as  below,  of  the  basic  conclusions  and 
recommendations,  to  include  both  certain  additional  information  as  yielded 
to  the  date  of  this  letter  by  a continuing  study,  and  also  comment  as  to 
further  investigation  indicated,  may  make  clearer  the  extent  of  present 
knowledge. 


SI 


NWCgtitATtON 


Conclusions:- 


Proven 


Proven 


Proven 


Concluded  from  analysis; 
suggested  as  a desirable 
operational  principle; 
needs  experimental  veri- 
fication. 


a ,n 


f « * y,  i 


i C ^ 


s^ujoi  i i %j 


a.  Weapon  employment  and  battlefield 
visibility  data,  show  the  limiting 
effect  upon  ranges  of  engagement 

for  the  rifle  of  both  combat  practice 
and  terrain  interruptions  to  the  line 
of  sight*  It  is  clearly  established 
that  the  relatively  short  ranges  pre- 
ponderate: "aimed11  rifle  fire  is 

delivered  at  ranges  less  than  300 
yards  about  three-quarters  of  the 
time*  There  is  only  a very  limited 
need  for  the  capability  for  such  fire 
at  greater  ranges.  Although  a distri- 
bution of  effect  which  does  not  exclude 
all  capabilities  at  those  greater 
ranges  is  required,  the  weapon  should 
be  designed  to  maximize  hit  probability 
at  the  more  common  ranges.  (The  infre- 
quent exceptions  include  the  sniping 
fire  of  specially  trained  and  equipped 
riflemen.  —Also,  it  should  be  noted 
that  bearing  upon  the  desirability  of 
adopting  a single  round  for  all  small 
arms  is  the  need  for  machine-gun  fire 
with  suitable  trajectory  and  adequate 
wounding  power  out  to  1800-2000  yards.) 

b.  In  the  man-rifle  combination,  aiming 
errors  are  generally  large— far  in  ex- 
cess of  purely  ballistic  dispersion. 
Thus,  if  at  any  extra  cost,  the  general 
purpose  weapon  need  not  be  designed  to 
provide  the  current  high  degree  of 
precision. 

c.  The  hill  automatic  feature,  in  rifles  of 
the  usual  design,  and  in  the  current  US 
experimental  models,  does  not  increase 
the  expectation  of  hitting  separated 
man-targets. 

d.  A controlled  dispersion  feature,  as  in- 
corporated in  a "salvo"  automatic  of  the 
type  proposed,  may  largely  compensate 
for  the  large  aiming  errors  which 
typically  accompany  each  trigger  pull. 


Unclassified 


S! 


SECUl 


'RMATiON 


Proven,  i 

at  Princeton  University,  the 
Army  Chemical  Center,  Aber- 
deen Proving  Ground,  and  else- 
where. Tests  of  bullets,  as 
contrasted  with  spherical 
pellets,  have  not  been  ex- 
tended beyond  the  range  of 
calibers  .30-. 21.  Additional 
experimentation,  through  a 
range  extended  downward,  is 
required  to  determine  the  best 
in.  i.3  it  ary  caliber,  from  'the 
standpoint  of  ’‘wounding  power” 
and  other  considerations. 


At  the  cost  of  a small  loss  in  armor 
penetrating  ability  at  some  ranges  (a 
characteristic  of  doubtful  military 
value  in  the  rifle),  a weapon  of  a 
caliber  smaller  than  .30,  providing 
a correspondingly  higher  velocity, 
offers  generally  superior  “wounding 
power"  at  the  ranges  of  interest 
(and  somewhat  beyond);  improved  ex- 
terior ballistics;  lighter  ammunition; 
a slightly  lighter  rifle i and  seme 
reduction  in  recoil.  The  small  cali- 
ber appears  especially  valuable  in 
connection  with  a "salvo"  automatic 
type  of  shoulder  weapon  which  projects 
four-  or  five-round  dispersion  patterns. 
Caliber  and  other  ammunition  charac- 
teristics within  the  following  ranges 
appear  to  offer  promise  of  substantial 
all-round  improvement: 

(1)  Caliber:  .276  (7mm)  - .180  (U.57mm). 

(2)  Wt.  ball:  lj.0-60  gr  (168  gr  for  cal- 

iber .30,  M2  AP). 

(3)  Wt.  charge:  U0-h5  gr  ($3  gr  for 

caliber  *30,  M2  AP). 


(li)  Wt.  complete  round:  250-300  gr  (1(16 
gr  for  caliber  .30,  M2 
AP). 

(5)  Muzzle  velocity:  3700-1:800  ft  per 

sec  (2770  ft  per  sec 
for  caliber  .30,  M2 
AP). 

(6)  Muzzle  energy:  1800-2200  ft-lb 

(2800  ft-lb  for  cali- 
ber .30,  M2  AP). 


Proven,  as  to  lethality  f. 

of  agent;  feasibility  of 
incorporation  in  the  round 
is  estimated  from  preliminary 
study  and  expert  opinion; 
relative  importance  of  disad- 
vantages has  not  been  weighed. 


/ /"x* 


sccu 


Toxic  agents  could  greatly  increase  the 
lethality  of  bullet  hits;  and  the  in- 
corporation of  such  agents  in  mass  pro- 
duced small  aims  ammunition  is  judged 
feasible.  Disadvantages  such  as  an  un- 
avoidable small  time  delay  in  producing 
the  lethal  effect,  and  the  ease  with 
which  the  enemy  could  retaliate  in 
kind,  as  well  as  the  relative  desir- 
ability of  killing  as  contrasted  with 


RMATION 


SE< 


INFORMATION 


wounding,  would  require  analysis  if 
a policy  decision  sanctioning  the  use 
of  such  agents  were  made. 


Recommendations 


Experiment  and  test  for  g. 

determining  details  of 
design,  for  verifying 
engineering  and  pro- 
duction feasibility, 
and  for  establishing 
jj t acceptability, 

&:?z-  necessary « 


0R0  recommends  the  manufacture  and  test 
of  experimental  weapons  and  ammunition 
in  sufficient  quantity,  and  of  a suf- 
ficient range  in  design  type,  to  permit 
conclusive  and  specific  determinations 
with  respect  tos 

(1)  Verification  of  the  operational 
value  of  a pattern  dispersion  feature 
(calculated  to  maximize  hitting  at  the 
ranges  of  concern)  in  a ’’salvo,”  or 
controlled  burst  cyclic,  automatic* 

(2)  Selection  of  the  best  smaller 
caliber  for  such  a weapon,  upon  the 
basis  of  all  functionally  associated 
characteristics . 

(3)  The  feasibility  of  designs  which 
afford  the  desired  characteristics, 
with  sufficient  reliability  in  pro- 
jecting the  chosen  dispersion  pattern, 
with  controlled  length  of  burst  if  a 
cyclic  weapon,  and  without  objection- 
able  cumulative  recoil  effects. 


U.  Further  experimentation  and  test  of  the  sort  indicated  need  not 
be  very  expensive  nor  time  consuming.  Certain  positive  information  of 
real  importance  and  immediate  application,  long  lacking  in  the  procedures 
by  which  military  characteristics  are  set,  and  rifles  and  ammunition  are 
designed,  could  be  provided  without  undue  effort.  Caliber,  for  example, 
has  been  the  subject  of  such  prolonged  controversy,  is  now  still  so  dis- 
puted within  the  NATO  (despite  a small,  measure  of  agreement  on  the  standard- 
ization of  ammunition  wrung  from  the  Standing  Group),  and  has.  in  the  past 
been  so  often  fixed  by  arbitrary  ruling,  that  it  is  high  time  all  the 
relevant  facts  as  to  caliber  and  ballistics  were  established  upon  a firm 
experimental  basis.  Again,  a positive  criterion  of  ’’wounding  power”  should 
be  found  and  related  to  tactical  employment  of  the  rifle.  Finally,  both  the 
design  and  performance  of  a shoulder  weapon  incorporating  the  novel  controlled 
dispersion  feature  should  be  put  to  actual  test* 


1 Incl 

ORO-T-160  (copies  2 to  10) 

Copies  (less  incl)  fhmished 
Director,  ORO 
Editor,  0R0 
Mr.  Norman  Hitcfaaan 


/s/  Edward  M.  Parker 

Edward  M ■ Parker 
Chairman,  Project  BALANCE 


SECURI 


DEPARTMENT  OF  THE  ARMY 

OFFICE,  ASSISTANT  CHIEF  OF  STAFF,  G-3,  OPERATIONS 

REGRADED  . BY  AUTHOI^™™  25 » D*  °* 

OF  CrU#*  5Z-1  AtjL 

3Y  Z ON  ^/30/^2_ 

G-3  040  ORO  (16  Dec  52)  8 January  1953 


SUBJECT:  Technical  Memorandum  0R0-T-160,  "Operational  Requirements  for 

An  Infantry  Hand  Weapon" 


70:  Commandant 

The  Army  War  College 
Carlisle  "arracks,  Pennsylvania 
ATTN:  Librarian 


1.  Transmitted  herewith  for  your  advance  information  is  one  copy 
of  Technical  Manor andum  0R0-T-160,  "Operational  Requirements  for  an 
Infantry  Hand  Weapon." 

2.  This  publication  is  a working  paper  of  the  Operations  Research 
Office  (Project  BALANCE),  in  which  consideration  is  given  to  the  desired 
capabilities  of  a modern  rifle.  The  Operations  Research  Office  makes 
one  particular  recommendation  already  approved  by  the  Chief  of  Staff, 
i.e.,  "that  a ma.U  (but  adequate)  number  of  experimental  weapons,  in- 
corporating the  desirable  characteristics  enumerated,  be  manufactured 
anfl  tested  by  the  Ordnance  Corps,  in  order  more  conclusively  to  determine 
the  military  value  of  the  suggested  features." 

3.  Request  that  appropriate  comments  on  this  Memorandum  be  sub- 
mitted to  ACofS,  G-3  (RRScSW)  for  consideration  by  the  Director  of  the 
Operations  Research  Office  in  the  preparation  of  the  final  report. 

FOR  THE  ASSISTANT  CHIEF  OF  STAFF,  G-3: 


1 Incl 
ORO-T-160 


Brigadier  General,  GS 
Deputy  ACofS,  G-3  for 
Research,  Requirements  & Special  Wpns. 


UNCLASSIFIED 


si